Classes of modules 1st Edition John Dauns

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Classes of modules 1st Edition John Dauns Digital Instant
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Author(s): John Dauns, Yiqiang Zhou
ISBN(s): 9781584886600, 1584886609
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File Details: PDF, 1.71 MB
Year: 2006
Language: english

Classes of Modules
Copyright 2006 by Taylor & Francis Group, LLC

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John Dauns and Yiqiang Zhou, Classes of Modules (2006)

John Dauns
Tulane University
New Orleans, Louisiana, U.S.A.
Yiqiang Zhou
Memorial University of Newfoundland
St. John’s, Canada
Classes of Modules
Boca Raton London New York
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Dauns, John.
Classes of modules / John Dauns, Yiqiang Zhou.
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ISBN-13: 978-1-58488-660-0 (acid-free paper)
ISBN-10: 1-58488-660-9 (acid-free paper)
1. Set theory. 2. Modules (Algebra) 3. Rings (Algebra) I. Zhou, Yiqiang. II.
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Contents
Preface v
Note to the Reader vii
List of Symbols ix
Chapter 1. Preliminary Background 1
1.1. Notation and Terminology 1
1.2. Lattices 5
Chapter 2. Important Module Classes and Constructions 7
2.1. Torsion Theory 7
2.2. Module Class σ[M] 12
2.3. Natural Classes 19
2.4. M-Natural Classes 24
2.5. Pre-Natural Classes 29
Chapter 3. Finiteness Conditions 33
3.1. Ascending Chain Conditions 33
3.2. Descending Chain Conditions 50
3.3. Covers and Ascending Chain Conditions 65
Chapter 4. Type Theory of Modules: Dimension 71
4.1. Type Submodules and Type Dimensions 71
4.2. Several Type Dimension Formulas 80
4.3. Some Non-Classical Finiteness Conditions 87
iii

iv
Chapter 5. Type Theory of Modules: Decompositions 107
5.1. Type Direct Sum Decompositions 108
5.2. Decomposability of Modules 117
5.3. Unique Type Closure Modules 132
5.4. TS-Modules 142
Chapter 6. Lattices of Module Classes 149
6.1. Lattice of Pre-Natural Classes 149
6.2. More Sublattice Structures 153
6.3. Lattice Properties of Np
r (R) 163
6.4. More Lattice Properties of Np
r (R) 177
6.5. Lattice Nr(R) and Its Applications 190
6.6. Boolean Ideal Lattice 200
References 205

Preface
The main theme of the book is in two concepts and how they pervade and
structure much of ring and module theory. They are a natural class, and a type
submodule. A natural class K of right modules over an arbitrary associative
ring R with identity is one that is closed under isomorphic copies, submodules,
arbitrary direct sums, and injective hulls. A submodule N of a right R-module
M is a type submodule if there exists some natural class K such that N ⊆ M
is a submodule maximal with respect to the property that N ∈ K. There are
also equivalent but somewhat technical ways of defining this notion totally
internally in terms of the given module M without reference to any outside
classes K. Equivalently a submodule N ≤ M is a type submodule if and only
if N is a complement submodule of M such that, for some submodule C ≤ M,
N and C do not have nonzero isomorphic submodules and N + C = N ⊕ C is
essential in M.
An attempt is made to make this book self contained and accessible to
someone who either has some knowledge of basic ring theory, such as beginning
graduate and advanced undergraduate students, or to someone who is willing
to acquire the basic definitions along the way.
A brief description of the contents of the book is given next. For some
readers such a description will only be useful after they have started reading
the book. The beginning Chapter 1 defines the more or less standard notation
used, and lists a few useful facts mostly without proof. Chapter 2 presents
all the module classes that will be used, among which are torsion, torsion free
classes, σ[M], natural classes, and pre-natural classes. Chapter 3 utilizes chain
conditions relative to some module class K of right R-modules. These chain
conditions guarantee that direct sums of injective modules in K are injective,
or that nil subrings are nilpotent in certain rings. Chapter 4 develops the
basic theory of type submodules, and the type dimension of a module, which
is analogous to the finite uniform dimension. Here new chain conditions, the
type ascending and descending chain conditions, are explained and used to
obtain structure theorems for modules and rings.
Chapter 5 shows that the collection N(R) of all natural classes of right R-
modules ordered by class inclusion is a Boolean lattice. By use of this lattice,
new natural classes are defined and used to give module decompositions of
a module M as a direct sum of submodules belonging to certain natural
classes. A module M is a TS-module if every type submodule of M is a direct
summand of M. Extending or CS-modules are a very special case of a TS-
module. A decomposition theory for TS-modules is developed which parallels
v

vi
the much studied theory of CS-modules. Chapter 6 studies the collection
Np
(R) of all pre-natural classes of right R-modules. This complete lattice is
significant in several ways. First of all, it contains almost all the well and
lesser known lattices of module classes as sublattices. Many sublattices of
Np
(R) are identified. Several connections between ring theoretic properties
of the ring R, and purely lattice theoretic properties of Np
(R), or some of its
many sublattices are proved. Thus, N(R) is a sublattice of Np
(R), but in
general not a complete sublattice. The interaction between a ring R and the
lattices associated to R is explored.
If ring theory is to progress, it seems that some new kind of finiteness or
chain conditions will be required, such as the type ascending and descending
chain conditions. Also, placing restrictive hypotheses on all submodules of
a module, or even only on all complement submodules, is too restrictive.
However, putting restrictions on the type submodules only is more reasonable.
At the time of this writing, this is the only book on the present subject.
Previously it was very inaccessibly scattered throughout the literature. More-
over, some results in the literature have been either improved or extended, or
proofs have been simplified and made more elegant.
We view this book not merely as a presentation of a certain theory, but
believe that it gives more. It gives tools or new methods and concepts to
do ring and module theory. So we regard the book as a program, a path, a
direction or road, on which so far we have only started to travel with still a
long way ahead.
The second author expresses his gratitude to his wife Hongwa and their son
David for their support and patience during this project, and he gratefully
acknowledges the support by the Natural Sciences and Engineering Research
Council of Canada.
John Dauns
Yiqiang Zhou

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Nov. 1.
severe, and Lieut.-Colonel Smith sent a message to Lord Bernard
Lennox: "Is your right still in touch with 4th Hussars? Brigadier
pressing for a reply." To which Lord Bernard answered, "Yes."
At 2.40 Lieut.-Colonel Smith sent the following request to the
Headquarters of the 4th Brigade:
Wood just short of D E near Canal is full of Germans, also Château de
Hollebeke. Can you turn on guns, please? My advance posts have been driven
in.
The Canal was dry, and formed no obstacle; and though there were
a few British cavalry this side of the embankment, they were not
enough to stop an attack. The French were said to be coming up to
strengthen this part of the line, but they did not arrive. Of all this
fortunately the Germans knew nothing, and instead of attacking this
weak spot, they directed their energies to the centre of the section
of the line held by the Grenadiers.
About 3 o'clock the enemy advanced in force through the wood near
the railway, but was met with such a withering fire from No. 1
Company that he did not succeed in getting very far. An hour later
Lord Cavan sent this message:
Well done. If absolutely forced back, retire as on parade with your proper
right, that is your left retiring, on line of railway. Put up the best fight you can
on edge of wood.
There was no need to retire, however,
although there was one moment at which
the situation seemed critical, for the Germans brought up some
field-guns, and plastered the trenches with every conceivable kind of
shell.
The shelling stopped shortly after dark, and the men were able at
last to look out over their trenches, and survey the scene by the
lights of a farm which was blazing in the centre of the line. They saw
a spectacle, which later on grew more and more familiar. What had
once been a field was now a mass of trenches; the whole place had

Nov. 1.
been ploughed up by shells, and the hedges were all torn up and
burnt and blown to bits.
During the night the 2nd Battalion
Grenadiers was relieved by a regiment from
the French Sixteenth Corps, and retired at 4 A.M. to the rear of
Zwarteleen, where the men thought they were going to get some
rest, but before very long they were on the move again. Sir Douglas
Haig had sent a message which Lord Cavan circulated as follows:
The German Emperor will arrive in the field to-day to conduct operations
against the British Army. The G.O.C. First Corps calls upon all ranks once
more to repeat their magnificent efforts and to show him what British soldiers
really are.
All the enemy's efforts were now concentrated on smashing the left
of the Irish Guards' trenches with high-explosive shells, and firing
with wonderful accuracy they gradually blew the trench in bit by bit,
and knocked out their machine-guns. At 3 P.M. Lord Cavan heard a
report that the Irish Guards were retiring, and that they had only
about 200 men left. He sent orders at once that they were at all
costs to hold on to the wood 200 yards in rear of their old line. The
French were told to stay where they were, as in the event of a
withdrawal the whole British line was to pivot on them on the elbow
of the Canal. The highest praise was afterwards given by the British
Generals to the French for the way in which they held their trenches
all day, in spite of the fact that their left was in the air.
An urgent appeal for help now reached Lord Cavan from one of the
Corps Staff, stating that the Northamptonshire Regiment was being
driven back and needed support. The 2nd Battalion Grenadiers was
immediately sent off with orders to report itself to General Bulfin,
who was to be found in a wood three-quarters of a mile south-west
of Herenthage. But by the time the Battalion arrived there General
Bulfin had been wounded, and Lieut.-Colonel Smith could not find
out what it was he was expected to do.

In the meantime Lord Cavan received orders to assume command of
the whole section from the east edge of the wood to the French left.
In these strenuous days it was no uncommon thing for an officer to
be told in the middle of a battle to take over command of a force
during a difficult operation—a war ordeal, for which peace training
had supplied no practice. To take over the command of a Division is
no easy matter at any time, but to do it at a critical moment, with
heavy fighting going on, demands a man of more than ordinary
capacity. Lord Cavan galloped up with his Brigade-Major, Major the
Hon. W. P. Hore-Ruthven; on arrival at General Bulfin's Headquarters
he found that everything had been momentarily disorganised by the
sudden departure of the wounded General. Officers of all sorts were
asking for orders. The Germans were breaking through. Perplexing
problems of every description were submitted for instant solution.
Shells were falling in the immediate neighbourhood of the Divisional
Headquarters. Very slowly Lord Cavan drew out his cigar-case, and
having carefully selected a cigar, proceeded to light it, turning it
round to see that it was evenly lighted. This had a wonderful effect
on all present, for it not only enabled Lord Cavan himself to
concentrate his thoughts on the problem, and to see clearly the
most pressing needs of the moment, but it also inspired all the
officers with confidence. As a Staff Officer, who was present, said
afterwards, that cigar saved the situation.
On the left the Sussex Regiment was in touch with the Seventh
Division, and stood firm. The Northamptonshire Regiment, Gordon
Highlanders, and Oxfordshire Light Infantry had all been pressed
back from their advanced trenches, though the enemy had not got
beyond them. Lord Cavan at once ordered the Grenadiers to leave
their packs at the farm in the rear of the Brown Road, and to clear
the wood south-east of that road at the point of the bayonet.
Thereupon Lieut.-Colonel Smith launched the Battalion with fixed
bayonets into the wood. It was very thick in places, and there was
always a risk of some company getting lost. The Germans, it was
found, had left the wood, but only recently, as was evident from the
number of dead. That the difficult manoeuvre, entrusted to the

Nov. 2.
Battalion, was carried out most successfully was due to the excellent
manner in which the four Captains led their men. One platoon of
Major Hamilton's company, which went beyond the wood and was
enfiladed by machine-guns, had to remain under cover of a bank till
dark, when it retired and joined the main line. With this exception
the companies—No. 1 under Major Hamilton, No. 2 under Lord
Bernard Lennox, and No. 3 under Captain Powell—all managed to
reach the edge of the wood in perfect order. No. 4 under Captain
Ridley was in support.
This advance had the excellent effect of establishing confidence.
Lord Cavan was able to reorganise the line of defence for the night,
and, by blunting the salients of the wood facing south-east, to
reduce the garrison. The result was that he withdrew two battalions
—one, the Sussex Regiment, was placed in reserve; the other, the
Gordon Highlanders, was sent back to the 20th Brigade, to which it
belonged.
As soon as it was dark, the Germans tried to set the wood on fire,
but fortunately did not succeed, though there were isolated fires in
various parts of it. It was an awkward position and very difficult to
hold, as the Germans were so close, but orders were received for
the battalions to dig in where they were. To officers, who had been
taught from their early youth that one of the essentials of a trench
line was a good field of fire, this digging in a thick wood, where the
field of fire was never more than from fifteen to twenty yards,
seemed an absurdity. But ideas on this subject had been
considerably revised by the war—besides, in a long line of trenches
running several miles, battalions of course must join up with each
other, and cannot choose a position for themselves.
At 10 o'clock that night, No. 4 Company, under Captain Ridley, was
directed to take over the position held by a company of the Gordons
on the left, but finding that the trench had almost vanished after a
day's work by the German artillery, it dug a new one slightly in rear,
which was not finished until 3 A.M.

This was the situation on the Monday morning: the
Northamptonshire Regiment was in touch with the Seventh Division
on the left; the Oxfordshire Light Infantry and Grenadiers, slightly
intermingled, were in the centre, and the Irish Guards on the right—
all holding the south-east edges of the wood. Four vigorous attacks
on the line—at 8.45, 11, 2, and 5.45—were delivered by the
Germans, preceded by heavy shelling, especially on the left. The
attack at 11 looked dangerous at one time, when the Germans got
within twenty-five yards of our trenches, but our fire was very
steady, and they could make no farther headway. The 2 o'clock
assault partially developed, but the one at 5.45, just after it got
dark, was the most serious.
It was directed against Captain Ridley's Company and against the
Oxfordshire Light Infantry, and the enemy advanced with a beating
of drums and blowing of horns. The night was cold, with some light
from the moon. As the enemy came on, an incident that was never
explained took place. The firing almost died down, and this
message, sent from no one knew where, was passed along the line:
"Don't fire. The Northamptons are going to charge." It so happened
that Lieut.-Colonel Smith and Major Jeffreys were in that part of the
trench at the time, and directly they heard the mysterious message
they realised it was a German ruse. They yelled at the men to go on
firing. The fire was at once taken up and continued, while the attack
died away. Next day Lieut.-Colonel Smith tried to discover where the
fictitious order started, but in vain.
All night the enemy could be heard digging away, in some places
near to our trenches. At 1 A.M., No. 4 Company was sent back in
reserve, being relieved by a company of the Oxfordshire Light
Infantry, which next morning reported that 300 dead had been
found in front of the trench. Some were found within a few yards of
our line.
On Monday evening, the night of the attack, this special order from
the Commander-in-Chief was circulated:

Nov. 3.
Nov. 4.
The Field-Marshal Commanding in Chief has watched with the deepest
admiration and solicitude the splendid stand made by the soldiers of His
Majesty the King in their successful effort to maintain the forward position
which they have won by their gallantry and steadfastness. He believes that no
other Army in the world would show such tenacity, especially under the
tremendous artillery fire directed against it. Its courage and endurance are
beyond all praise. It is an honour to belong to such an Army.
The Field-Marshal has to make one more call upon the troops. It is certainly
only a question of a few days, and it may be of only a few hours, before, if
they only stand firm, strong support will come, the enemy will be driven back,
and in the retirement will suffer losses even greater than those which have
befallen him under the terrific blows by which, especially during the last few
days, he has been repulsed.
The Commander-in-Chief feels sure that he does not make his call in vain.
J. D. P. French, Field-Marshal,
Commander-in-Chief to the British Army in the Field.
A comparatively quiet interval followed.
There was intermittent shelling next day,
though nothing very serious, and the snipers on both sides kept up a
lively fusillade. The trenches meanwhile were deepened and
improved. Some new orders with regard to the coming fighting were
also issued. Each battalion had two companies in the firing line and
two in support, and the captains were told that they must rely on
their own supports if they wanted any help. There was a Cavalry
Brigade in reserve, but Lord Cavan did not wish to call on it unless it
became absolutely necessary. Another warning against the enemy's
tricks was sent to the men in this message from G.O.C. First Corps:
First Cavalry Division reports that in the attacks on them the Germans wore
British uniforms, especially kilts, and when approaching our trenches shouted,
"Don't fire; we are short of ammunition," and similar expressions. All troops in
the trenches are to be warned of this practice by the enemy.
An instruction was issued also for the making of circular redoubts,
about twenty-five yards in rear of the existing line of trenches, with
the object of stopping a rush if the line should be pierced.

Nov. 5.
Nov. 6.
An artillery duel—rather one-sided—occupied the next two days. A
German aeroplane having located the trenches, the enemy's guns
became very busy, though mostly against the support trenches,
chiefly with the object of "searching the ground." Early in the
afternoon the First Division reported that the enemy was attacking
from the direction of the woods south of Gheluvelt. The artillery had
been turned on them, and preparations were being made to meet
the attack, but nothing came of it. The shelling stopped at nightfall,
and the Battalion settled down to a pitch-dark, pouring wet night in
the trenches, which were all in wet clay and marshy ground, and the
men's sole consolation was that the Germans must be having just as
bad a time.
By the 5th it began to be thought in the
firing line that the enemy had abandoned
all attempt to break through the line, but in reality he was waiting
only for reinforcements. He had succeeded in making a dent in the
line near Messines, and was now determined to throw the whole
weight of his superior numbers on Ypres. He chose for his point of
attack Klein Zillebeke, the junction between De Moussy's French
Division and the 4th Brigade, or rather the four battalions under Lord
Cavan.
Shelling began with renewed vigour as soon
as the sun had cleared away the next
morning's mist, and just before mid-day significant instructions were
received from Lord Cavan:
"Your position must be retained at all costs," he said in a message sent out at
11.50. "Redoubts must be occupied, every spare man and tool employed to
make secondary trench. I trust you after splendid defence of last few days to
maintain it to the end."
And in a second message a few minutes later:
"Have asked Seventh Division to do everything possible to help you with
artillery fire."

Evidently the Brigadier expected a determined attack on that part of
the line, and Lieut.-Colonel Smith made his dispositions accordingly.
Early in the afternoon he got a report from the Irish Guards that the
French Division on their right had been driven in. Immediately
afterwards came a message from Major Hamilton that the Irish
Guards themselves had been driven in, and that his right was
consequently in the air.
Major Hamilton's Company was now bearing the brunt of the attack,
and was in a very critical position. Lieut.-Colonel Smith sent word to
ask him whether he needed any help. He replied: "Hughes only
wants a few men, and I have sent him up one section. Bailey is
lining road 200 yards to my front. O.C. Oxfords promised support if
necessary."
Shortly afterwards it was reported that the Germans had reached
Brown Road, and were advancing round the right rear of the
Battalion. Lieut.-Colonel Smith at once posted Lieutenant Tufnell with
one machine-gun on the Brown Road, to guard the ride through the
wood across which the enemy would have to pass, to get behind our
line of trenches, telling him to use his own discretion as to the
position he should take up. Lieutenant Lord Congleton was also sent
with one platoon to stop the Germans from getting through a gap
which was reported to the right rear of the Battalion. Lieutenant
Tufnell apparently decided that he would be able to get a better
target for his machine-gun, and at the same time guard the ride, if
he accompanied Lord Congleton. He accordingly took up a position
from which he could command the advancing enemy, but had not
been there long before he was mortally wounded.
At this point Lieut.-Colonel Smith reported to Lord Cavan that it was
urgently necessary that a farm to his front should be destroyed, as
there were machine-guns firing from it. He received the reply that if
it were humanly possible the howitzers would do as he asked.
Two companies of the Sussex Regiment were now sent up to
support the right of the line, and helped to hold things together, but
the situation was most critical. The enemy had driven back De

Moussy's French infantry, and consequently there was a bad dent in
the line. Lord Cavan's troops were still holding on with their right in
the air when the Household Cavalry was called in to retrieve the
situation. Lord Cavan sent off Captain R. C. de Crespigny, his Staff
Captain, at full gallop to Sanctuary Wood with orders to the
Household Cavalry to come up at once. Colonel Wilson immediately
ordered his men to mount, and galloped round by Maple Copse to
within 500 yards of Brigade Headquarters, where they dismounted
and fixed bayonets. Into the midst of the Germans they dashed,
headed by Colonel Gordon Wilson.
Throwing in the cavalry at the critical moment to save the situation
has from time immemorial been a recognised tactical manoeuvre,
but in this case the Household Cavalry fought as infantry, and very
splendid infantry they made. They swept forward to the attack with
all the precision of an infantry battalion, and soon Klein Zillebeke
was filled with British, French, and German troops fighting at close
quarters. When it came to hand-to-hand fighting, the Germans could
not stand up against the splendid men of the Household Cavalry, and
they were gradually driven back till the line was restored. This
gallant charge of the Household Cavalry on foot, Lord Cavan
afterwards said, not only prevented the 4th Guards Brigade from
being cut to pieces, but also saved Ypres. Colonel Gordon Wilson
and Colonel Hugh Dawnay were killed, and the Household Cavalry
lost a large number of men, but the situation was retrieved.
While this was going on, No. 1 Company Grenadiers, which was on
the right, had been practically wiped out. Since the withdrawal of the
Irish Guards, almost every man had been killed or wounded by shell-
fire. Sergeant Thomas, who commanded the right platoon of No. 1,
remained at his post after the Irish Guards had gone, until he had
only three men left, when he withdrew to Brown Road. During that
time he was twice buried by shells, and had three rifles broken in his
hand. Sergeant Digby was mortally wounded, and was never seen
again.

Lord Cavan telephoned: "Hang on tight to Brown Road. Try and get
touch with half battalion Sussex Regiment sent to farm at Irish
Guards H.Q." Lieut.-Colonel Smith passed this on to Captain Powell,
adding: "Are you in touch with the Sussex?" to which Captain Powell
replied: "Yes, I am in touch with Sussex, who prolong my line to the
right, bent back to right rear."
In the meantime, Lieutenant Lord Congleton, finding how weak the
right of the line was, had moved his platoon to the right of the
Sussex. He had lost a number of men, but at the same time had
managed to collect several Irish Guardsmen. They had no rifles or
ammunition, but he placed them at intervals among the men of his
platoon, and went and collected rifles for them himself from the
casualties. Then he went round a second time with an orderly and
collected ammunition. By this means he was able to hold the gap all
through that night, and next day was specially mentioned by Lieut.-
Colonel Smith, who wrote that the intelligent way in which he
handled his platoon on his own initiative was beyond all praise.
Much help towards keeping the right of the line intact was also given
by Colonel Davies, commanding the Oxfordshire Light Infantry, who
throughout the afternoon kept sending up any men he happened to
have in reserve.
When darkness fell Lord Cavan gave Lieut.-Colonel Smith these
directions:
Can you establish a line between the Brown Road and your original line so as
to keep touch for certain with battalions on your left? I want to make sure
that my line for the night is in touch all along. I have ordered two battalions
to establish the line of the Brown Road up to south-west edge, where I hope
to establish touch with the French. I have told General Kavanagh he can
withdraw his Cavalry Brigade directly the whole of the Brown Road is
established.
The new line was arranged about midnight, and at 1 A.M. the men
began to dig, although they were dead tired. The trenches were
completed by 4 A.M.—a fine performance on a pitch-dark night, with
the additional handicap of the trees.

Nov. 7-9.
Nov. 10.
For three days the battalions remained in
their trenches at Klein Zillebeke without any
direct attack being made. Shelling went on all day with monotonous
regularity, but on the whole little damage was done, though the
German howitzers made spasmodic efforts to demolish the trenches,
and occasionally managed to blow in a bit of trench and bury some
men. The nights were comparatively quiet except for some sniping,
and though the mornings were generally foggy, anything in the way
of dirty weather was welcomed by the men, as it made artillery
observation impossible.
The shelling increased enormously on the
10th, and owing to the right having been
thrown back, that part of the trenches was open to enfilade fire from
the German guns. By this time their artillery had the range of our
trenches pretty accurately, and obtained a large number of direct
hits. Further, the wood, always a trouble, became more and more
difficult to hold: trees cut down by the shells fell crashing to the
ground, and made communication impossible. About mid-day the
bombardment became terrific, and it seemed as if it would be
impossible for any one to live under the storm of shells.
A heavy loss this day was the death of Major Lord Bernard Lennox,
who was killed by a high-explosive shell. For three months he had
been in the thick of every engagement, always cheerful, and making
the best of every hardship. He was one of the most popular officers
in the Brigade of Guards, and his death was very keenly felt by every
one.
Lieutenant M. G. Stocks was also killed by a shell, and Lieutenant
Lord Congleton, who had so distinguished himself only a few days
before, was shot through the heart. Lieutenant H. R. C. Tudway was
hit in the head by a shell, and died a few days later. Captain Powell
was buried by another shell, and was only just saved in time and
brought in. Captain Ridley was wounded in the back, but after being
attended to in the dressing-station was able to return to his
company.

There was considerable delay in collecting the wounded. It was
impossible to attempt to work by day, and the difficulties of carrying
stretchers by night were increased by the fallen trees.
That night the Battalion went into Corps Reserve, and bivouacked in
dug-outs. Lord Cavan, in writing an account of the day's fighting,
said:
The 2nd Battalion Grenadiers made a wonderful stand to-day against enfilade
fire of the worst description. They stuck it out simply magnificently.
The King subsequently telegraphed to the Commander-in-Chief:
The splendid pluck, spirit, and endurance shown by my troops in the
desperate fighting which has continued for so many days against vastly
superior forces fills me with admiration. I am confident in the final results of
their noble efforts under your able command.
George R.I.
Sir John French replied:
Your Majesty's most gracious message has been received by the officers and
men of Your Majesty's Army in France with feelings of the greatest gratitude
and pride. We beg to be allowed to express to Your Majesty our most faithful
devotion and our unalterable determination to uphold the highest tradition of
Your Majesty's Army, and to carry the campaign to a victorious end.
Lord Kitchener telegraphed:
The splendid courage and endurance of our troops in the battle in which you
have been engaged during the last few days, and the boldness and capacity
with which they have been led, have undoubtedly given the enemy a severe
blow, successfully frustrating their efforts. Let the troops know how much we
all appreciate their services, which worthily maintain the best traditions of our
Army.
Having been placed in Corps Reserve for four days, officers and men
of the Battalion were under the impression that they were going to
have a quiet time for that period, sleeping in peace at night and
resting during the day. But they were mistaken. In reality, they spent
three of the nights marching about the whole time, and each day

Nov. 11.
they were moved up in support of this or that part of the line, to the
invariable accompaniment of considerable shelling. To begin with,
the relief took most of the first night, and it was not till 5 A.M. that
the Welsh Regiment and Munster Fusiliers finished taking over the
trenches. Then at last the Battalion was able to march over to the
dug-outs at Bellewaardes Farm, north of Hooge.
The worst of it was that those placed in
reserve were at the beck and call of any
General who wanted reinforcements. At one time the Battalion was
placed under four Generals, and received different orders from each,
which came about because the units in front got hopelessly mixed,
and the battalions were constantly changed from one brigade to
another. For instance, when the 2nd Battalion Grenadiers arrived at
Bellewaardes, Lieut.-Colonel Smith rode over to see General Monro,
who congratulated him on the good work his men had done, and
said he would come round later and say a few words to them. By the
time Lieut.-Colonel Smith returned, he found that the Battalion had
been ordered to move to a wood north-east of Hooge Château, in
order to be in a position of readiness to reinforce the line near
Polygon Wood, where the Prussian Guard was reported to have
broken through. He sent one company up into the wood, and
scattered the rest about the grounds of the Château. It was chiefly
shrapnel-shelling that they were exposed to during this operation,
and there were few casualties.
In the afternoon orders were received to support an attack which
was to be carried out by the Sussex Regiment, Oxfordshire Light
Infantry, and Gloucester Regiment. They were to retake the trenches
which had been captured by the Prussian Guard in the morning,
south-west of Polygon Wood. The Battalion was severely shelled, as
it crossed the open ground towards the wood east of Hooge in
artillery formation, and had thirty to forty casualties in a few
minutes. Then Lieut.-Colonel Smith sent Major Jeffreys forward to
find General FitzClarence, under whose orders the Battalion had
been placed.

Nov. 12.
The enemy now began to shell this spot with shrapnel, and with
every one underground it was no easy matter to find the General or
his Staff. Major Jeffreys was joined by Lieut.-Colonel Smith; they
searched and searched in vain, and came across Major Corkran,
Brigade-Major of the 1st Brigade, who had been engaged on the
same fruitless errand. Deciding to wait, Lieut.-Colonel Smith sent
Major Jeffreys back to the Battalion, where he found Captain Pike,
who was almost immediately afterwards wounded by a shell.
Meanwhile the Battalion had been waiting for hours under shell-fire,
and had suffered about thirty further casualties. It was now night,
pitch-dark, and pouring with rain; and to assemble the men, who
were spread out in artillery formation, was by no means easy, but
Major Jeffreys managed to get them together near Nonne-Bosschen
Wood. Eventually Lieut.-Colonel Smith found General FitzClarence,
and got permission to give the men a meal before taking them up to
the front. Having returned to the Battalion, he marched it back to
the Château grounds, where after some delay the cookers arrived,
and the men settled down to a meal in the pouring rain. Lieutenant
the Hon. W. R. Bailey was appointed Adjutant in Captain Pike's
place, and at once took over his duties.
After an hour's sleep the Battalion started
off again at midnight, and marched ankle-
deep in mud and slush to the Headquarters of the 1st Brigade,
where it received its orders for the attack in which it was to operate
with the 1st Battalion Irish Guards, Royal Munster Fusiliers, and
Gloucester Regiment.
These orders were:
The following move at 2.15 A.M., to position of readiness at S.W. corner of
Polygon Wood—2nd Battalion Grenadiers, 1st Battalion Irish Guards, Royal
Munster Fusiliers. Left of Grenadier Guards and right of Irish Guards at S.W.
corner of Polygon Wood, both in column of route heading south. Royal
Munster Fusiliers on edge of wood just in rear of centre. When ordered to
move from position of readiness to attack, Grenadiers will lead in file, passing
along western side of trench and shooting any enemy met with either in or
out of it. Irish Guards to follow Grenadiers in same formation, Royal Munster

Fusiliers to follow Irish Guards. When trench has been cleared, Battalions will
occupy and hold it till further orders. Attack will be ready to start any hour
after 4 A.M. All movements to be made quickly and silently. Reports to H.Q. 1st
Guards Brigade. Captain Fortune, Black Watch, will act as guide to Grenadiers.
Battalions in rear will keep touch with Battalions in front of them. Gloucesters
will fill gap as at present.
At 3 A.M. these battalions started. It had been arranged that the Irish
Guards should lead as far as Polygon Wood, and General
FitzClarence and his Staff walked at their head. In spite of the
darkness the battalions kept well together. They were marching
down a muddy lane when suddenly some shots were heard in front,
and General FitzClarence halted his force and went to see what was
going on. The advance began again slowly, they reached the west
edge of the wood, and the Grenadiers got into the ditch at the edge.
Then came the news that General FitzClarence had been mortally
wounded. Colonel Davies arrived next with the Oxfordshire Light
Infantry, having reconnoitred the positions; he had found that the
Germans were in great strength, with wire entanglements in front
and several machine-guns.
The question now arose: What should be done? Was it wise to carry
on the attack with no General in command? Eventually the matter
was referred to Brigadier-General Westmacott, commanding the 5th
Brigade. He decided that it would be best to abandon the attack, as
after this delay there would not be enough time for it to develop
before daybreak. He therefore ordered the battalions back behind
the wood, west of Nonne-Bosschen Wood, and determined to hold a
new line. Colonel M'Ewen of the Camerons was sent for, to take
command of the Brigade.
The work of digging the new line was entrusted to the Gloucesters,
but as they were not strong enough to hold it, No. 4 Company
Grenadiers under Captain Ridley was sent up to reinforce them.
Tired as the men were, they dug for their lives, and by 6 A.M. had
managed to dig themselves well in. The rest of the Battalion
returned to the Château, where it was found that in the darkness

Nov. 13-14.
Nov. 15-16.
one platoon of No. 1 Company and the Battalion Headquarters had
gone astray. However, they arrived next morning.
After having been placed under several different Brigadiers, the
Battalion was finally ordered by Colonel Cunliffe Owen to move with
the Irish Guards to the wood on the Menin road, and there dig itself
in. Off it went, and began digging again till the dawn broke, when
the shelling started again as usual. This was the only day on which
the Battalion had no rations, the constant moves having
disorganised the transport, but enough bully beef was procured to
give the men something to eat.
During the day the Battalion remained in its
trenches. There was the inevitable shelling
and sniping, but little damage was done. In the evening it moved
back to within a mile of the Château, and was just settling down
when it received orders to move on to Sanctuary Wood—so called
because it had never been shelled. After some delay, it got to the
wood in the middle of the night, finding there some howitzers which
had been attracted by the name. The officer in command explained
that they had been shelled out of every place they had visited
hitherto by the bigger guns of the enemy. Before long, however, the
German artillery located the howitzers, and at once began to shell
the wood. While Major Hamilton was in his dug-out, a high-explosive
shell brought the whole structure down on him, and he was dug out,
unconscious, only just in time. Not long afterwards Lieutenant
Dowling was wounded.
In the middle of the next night the Battalion was ordered to return
to the trenches and join the 4th Brigade. Its four days' "rest" was
over, and all ranks welcomed with enthusiasm the prospect of
getting back to the trenches!
Next day the Battalion marched back
through Zillebeke to Lord Cavan's
Headquarters, and was at once sent back into the trenches, part of
which it had held the week before. The companies were sent up on
each side of the Cavalry Brigade, which was holding a line across

Nov. 17.
Brown Road, and the Battalion was therefore split up into two
portions. Nos. 4 and 2 Platoons of No. 3 Company were on the left
of the cavalry, and Nos. 1 and 2 Companies on the right; the only
reserve there was consisted of two platoons of No. 3 Company, and
so they "carried on" for two days without any happenings of great
importance. The weather meanwhile became very cold, and there
were continual snow blizzards.
On November 17 the Germans made their
last serious attack on Ypres. The day
opened with a terrific bombardment, evidently heralding a
determined attack. The shelling went on steadily all the morning,
and about 1 P.M. the attack started, the brunt of it falling on No. 1
and No. 2 Companies. No. 2 in particular was very hard pressed.
Captain Symes-Thompson was killed, and Lieutenant Lee-Steere,
who took over the command, sent back word that they were running
short of ammunition. There were but two platoons in reserve, and
they numbered only thirty men, but Lieut.-Colonel Smith sent them
up under Captain Cavendish with some ammunition. By the time
they arrived Lieutenant Lee-Steere had been killed. Captain
Cavendish sent back a message that the enemy was apparently
entrenching in a spinney about four hundred yards to our front, and
that his numbers were estimated at 500. About this time the enemy
attacked in great force, but was quite unable to make any headway
against our rifle-fire. The spirits of the men were wonderful, and
they fought on, quite unaffected by the terrible casualties caused by
the shell-fire amongst their ranks. Captain Cavendish was surprised
at suddenly hearing a burst of firing intermingled with shouts of
laughter. It turned out that some Germans, who had lain down in a
slight fold in the ground when their attack failed, were trying to
crawl back, and the men of Nos. 2 and 3 Companies were firing at
them as they went. The enemy was now becoming very numerous in
front, and the situation was reported to Lord Cavan by Lieut.-Colonel
Smith, who received this reply:
Call on 1st Battalion Coldstream for help if required at once. Brigade
Headquarters knocked to bits, so have shifted to farm north-west of wood, on

Figure 17 of K 17, in dug-out.
A little while afterwards the situation was easier, and on hearing that
the line was still intact, Lord Cavan sent the message:
Well done. Hope you got my memo, re calling on 1st Battalion Coldstream at
once if necessary, now in the wood alongside of you. You must use them to
help both yourself and the Irish Guards. When called on let me know. Am
turning all the artillery on the wood to your front. I have no means of
communication left except orderlies.
The 1st Battalion Coldstream at that time consisted of a draft of 300
men under Captain G. Edwards, which had just arrived from
England, the Battalion having been practically wiped out in the
Prussian Guard attack of November 4.
No. 1 Company was now in a bad way, and Captain Hughes sent
back an urgent request for more ammunition. But, as most of the
pack animals had been killed in the morning's bombardment, it was
a problem how to send it. Major Jeffreys collected as many orderlies
as he could find, loaded them up with all the ammunition they could
carry, and himself led them along to the trenches. This was no easy
matter, as not only was the ground they had to cross under shell-
fire, but the whole place was knee-deep in mud. The last fifty yards
to the trenches they had to crawl.
The firing had been kept up practically all the afternoon, and some
idea of the amount of ammunition expended may be gathered from
the fact that No. 1 Company alone fired 24,000 rounds. This was the
first time our men saw the hand grenades which were to play such a
large part in trench warfare. Little puffs of smoke had been
occasionally seen bursting on the bodies of the Germans, and these
proved to be caused by hand grenades of a primitive type, which
exploded when hit by our bullets.
By the evening the German attack had died down. The enemy had
lost very heavily, and realised, apparently, that the line was too
strongly held for any frontal attack to succeed:

The casualties amongst the officers of the 2nd Battalion were
unfortunately heavy:
Captain E. J. L. Pike (Adjutant), wounded.
Lieut. C. W. Tufnell (Machine-gun Officer), killed.
Capt. C. Symes-Thompson (No. 1 Company), killed.
Major Lord Bernard Gordon-Lennox (No. 2 Company), killed.
Lieut. I. St. C. Rose (No. 2 Company), wounded.
Lieut. C. M. C. Dowling (No. 2 Company), wounded.
2nd Lieut. F. W. J. M. Miller (No. 2 Company), killed.
2nd Lieut. J. H. G. Lee-Steere (No. 2 Company), killed.
Capt. E. G. H. Powell (No. 3 Company), wounded.
Lieut. H. R. C. Tudway (No. 3 Company), killed.
Lieut. Lord Congleton (No. 3 Company), killed.
Captain M. E. Makgill-Crichton Maitland (No. 4 Company),
wounded.
Captain E. D. Ridley (No. 4 Company), wounded.
Lieut. M. G. Stocks (No. 4 Company), killed.
The 2nd Battalion had been fighting incessantly from October 21 to
November 16. Day and night it had been attacked by an enemy
greatly superior in numbers. As it had never for a moment been able
to leave the front line, its sleep had been broken and scanty. Yet well
aware that no reinforcements were available, the Battalion had
throughout realised that it must continue to hold the line, and had
faced its task with the utmost determination. Even when it was in
reserve, it had taken part in serious engagements, but this to a
certain extent was an experience which it shared with the other
battalions of the 4th Brigade.
The 2nd Battalion Grenadiers had been most fortunate in its
neighbours during these strenuous days, and the men soon found
that the other battalions in the Second Division were as stout
fighters as themselves. The 2nd Battalion Oxfordshire and
Buckinghamshire Light Infantry in particular was known throughout

Nov. 19.
the Division as one of the best battalions in the Expeditionary Force,
and the Grenadiers knew from experience that it could be relied
upon to hold a trench to the last man.
But perhaps the branch of the service which won the men's
admiration most of all was the artillery. Outnumbered and
outranged, the Second Division artillery fought on, and time after
time saved the situation. Its supply of shells, compared to that of
the German artillery, was ridiculously small, and yet never for a
moment did it fail to respond when called upon to support the
infantry attacks. According to all preconceived theories it should
have been wiped out altogether, and in fact many batteries were
annihilated. But the Grenadiers knew that as long as there were any
men left alive the guns would be served.
The first battle of Ypres may be said to
have ended on the 19th, although naturally
the enemy continued his shelling. Some of No. 1 Company's
trenches were blown in, but there were no infantry attacks. In the
evening the 2nd Battalion Grenadiers was relieved by the 3rd
Battalion Coldstream and marched to St. Jean, where one company
went into billets, and the other three lay in the open and made
themselves as comfortable as they could with straw, which they took
from the ricks at the farm close by. Curiously enough, the farmer
some twelve months later sent in a claim for compensation for the
straw that had been taken. The few remaining officers managed to
get into one room at the farmhouse.
It was bitterly cold, and there were several degrees of frost and two
or three inches of snow on the ground. Before leaving, Lieut.-Colonel
Smith sent the following message to Captain Cavendish:
If it is possible, will you try and identify some of the units which attacked you
yesterday? Perhaps you could get a few shoulder-straps after dark, but you
are not to risk life to get them. I do not want to support you unless it is
necessary, but I can send a platoon of the Coldstream to a place near Irish
Guards' support if you would like it. You will be relieved by Coldstream to-
night about 8 P.M. after your teas, and will come to Brigade Headquarters

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