Mixing
how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$? [duplicate]
$begingroup$
This question already has an answer here:
If $m$ divides $n$, find a free resolution of $mathbb{Z}/m$ as a $mathbb{Z}/n$-module.
1 answer
can somebody please explain how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$??
abstract-algebra homological-algebra
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
asked Jan 24 at 17:53
user220607user220607
42
$endgroup$
marked as duplicate by Namaste abstract-algebra
Users with the abstract-algebra badge can single-handedly close abstract-algebra questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Jan 24 at 20:27
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
If $m$ divides $n$, find a free resolution of $mathbb{Z}/m$ as a $mathbb{Z}/n$-module.
1 answer
can somebody please explain how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$??
abstract-algebra homological-algebra
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
asked Jan 24 at 17:53
user220607user220607
42
$endgroup$
marked as duplicate by Namaste abstract-algebra
Users with the abstract-algebra badge can single-handedly close abstract-algebra questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Jan 24 at 20:27
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
$begingroup$
Is $Bbb Z_4$ a $Bbb Z_2$-module?
$endgroup$
– Lord Shark the Unknown
Jan 24 at 17:54
$begingroup$
What's wrong with the usual method? 1) Set $M=$ the module you want to resolve. 2) Write $M$ as a quotient of a free module. 3) Identify the kernel $N$ of the quotient map you got in step 2. 4) If $N=0$ stop, you are done. Otherwise, set $M=N$ and go back to step 2.
$endgroup$
– Jyrki Lahtonen
Jan 24 at 18:30
add a comment |
$begingroup$
This question already has an answer here:
If $m$ divides $n$, find a free resolution of $mathbb{Z}/m$ as a $mathbb{Z}/n$-module.
1 answer
can somebody please explain how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$??
abstract-algebra homological-algebra
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
asked Jan 24 at 17:53
user220607user220607
42
$endgroup$
This question already has an answer here:
If $m$ divides $n$, find a free resolution of $mathbb{Z}/m$ as a $mathbb{Z}/n$-module.
1 answer
can somebody please explain how to construct free resolution of the $ℤ_{4} $ module $ℤ_{2}$??
This question already has an answer here:
If $m$ divides $n$, find a free resolution of $mathbb{Z}/m$ as a $mathbb{Z}/n$-module.
1 answer
abstract-algebra homological-algebra
abstract-algebra homological-algebra
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
asked Jan 24 at 17:53
user220607user220607
42
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
asked Jan 24 at 17:53
user220607user220607
42
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
edited Jan 24 at 18:25
Jyrki Lahtonen
110k13171386
110k13171386
asked Jan 24 at 17:53
user220607user220607
42
asked Jan 24 at 17:53
user220607user220607
42
asked Jan 24 at 17:53
user220607user220607
42
42
marked as duplicate by Namaste abstract-algebra
Users with the abstract-algebra badge can single-handedly close abstract-algebra questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Jan 24 at 20:27
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Namaste abstract-algebra
Users with the abstract-algebra badge can single-handedly close abstract-algebra questions as duplicates and reopen them as needed.
StackExchange.ready(function() {
if (StackExchange.options.isMobile) return;
$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() {
var $hover = $(this).addClass('hover-bound'),
$msg = $hover.siblings('.dupe-hammer-message');
$hover.hover(
function() {
$hover.showInfoMessage('', {
messageElement: $msg.clone().show(),
transient: false,
position: { my: 'bottom left', at: 'top center', offsetTop: -7 },
dismissable: false,
relativeToBody: true
});
},
function() {
StackExchange.helpers.removeMessages();
}
);
});
});
Jan 24 at 20:27
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
$begingroup$
Is $Bbb Z_4$ a $Bbb Z_2$-module?
$endgroup$
– Lord Shark the Unknown
Jan 24 at 17:54
$begingroup$
What's wrong with the usual method? 1) Set $M=$ the module you want to resolve. 2) Write $M$ as a quotient of a free module. 3) Identify the kernel $N$ of the quotient map you got in step 2. 4) If $N=0$ stop, you are done. Otherwise, set $M=N$ and go back to step 2.
$endgroup$
– Jyrki Lahtonen
Jan 24 at 18:30
add a comment |
1
$begingroup$
Is $Bbb Z_4$ a $Bbb Z_2$-module?
$endgroup$
– Lord Shark the Unknown
Jan 24 at 17:54
$begingroup$
What's wrong with the usual method? 1) Set $M=$ the module you want to resolve. 2) Write $M$ as a quotient of a free module. 3) Identify the kernel $N$ of the quotient map you got in step 2. 4) If $N=0$ stop, you are done. Otherwise, set $M=N$ and go back to step 2.
$endgroup$
– Jyrki Lahtonen
Jan 24 at 18:30
1
1
$begingroup$
Is $Bbb Z_4$ a $Bbb Z_2$-module?
$endgroup$
– Lord Shark the Unknown
Jan 24 at 17:54
$begingroup$
Is $Bbb Z_4$ a $Bbb Z_2$-module?
$endgroup$
– Lord Shark the Unknown
Jan 24 at 17:54
$begingroup$
What's wrong with the usual method? 1) Set $M=$ the module you want to resolve. 2) Write $M$ as a quotient of a free module. 3) Identify the kernel $N$ of the quotient map you got in step 2. 4) If $N=0$ stop, you are done. Otherwise, set $M=N$ and go back to step 2.
$endgroup$
– Jyrki Lahtonen
Jan 24 at 18:30
$begingroup$
What's wrong with the usual method? 1) Set $M=$ the module you want to resolve. 2) Write $M$ as a quotient of a free module. 3) Identify the kernel $N$ of the quotient map you got in step 2. 4) If $N=0$ stop, you are done. Otherwise, set $M=N$ and go back to step 2.
$endgroup$
– Jyrki Lahtonen
Jan 24 at 18:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
A free resolution is given by
$$
dots xrightarrow 2 mathbb Z /4xrightarrow 2 mathbb Z/4xrightarrow 2 mathbb Z/4 rightarrow mathbb Z/2,
$$
where the last map is enlargement of cosets and, by a standard abuse of notation, $2$ denotes the map $bar 1mapsto bar 2$ (where bar denotes residue class). See the answer to this question.
answered Jan 24 at 18:14
o.h.o.h.
6217
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A free resolution is given by
$$
dots xrightarrow 2 mathbb Z /4xrightarrow 2 mathbb Z/4xrightarrow 2 mathbb Z/4 rightarrow mathbb Z/2,
$$
where the last map is enlargement of cosets and, by a standard abuse of notation, $2$ denotes the map $bar 1mapsto bar 2$ (where bar denotes residue class). See the answer to this question.
answered Jan 24 at 18:14
o.h.o.h.
6217
$endgroup$
add a comment |
$begingroup$
A free resolution is given by
$$
dots xrightarrow 2 mathbb Z /4xrightarrow 2 mathbb Z/4xrightarrow 2 mathbb Z/4 rightarrow mathbb Z/2,
$$
where the last map is enlargement of cosets and, by a standard abuse of notation, $2$ denotes the map $bar 1mapsto bar 2$ (where bar denotes residue class). See the answer to this question.
answered Jan 24 at 18:14
o.h.o.h.
6217
$endgroup$
add a comment |
$begingroup$
A free resolution is given by
$$
dots xrightarrow 2 mathbb Z /4xrightarrow 2 mathbb Z/4xrightarrow 2 mathbb Z/4 rightarrow mathbb Z/2,
$$
where the last map is enlargement of cosets and, by a standard abuse of notation, $2$ denotes the map $bar 1mapsto bar 2$ (where bar denotes residue class). See the answer to this question.
answered Jan 24 at 18:14
o.h.o.h.
6217
$endgroup$
A free resolution is given by
$$
dots xrightarrow 2 mathbb Z /4xrightarrow 2 mathbb Z/4xrightarrow 2 mathbb Z/4 rightarrow mathbb Z/2,
$$
where the last map is enlargement of cosets and, by a standard abuse of notation, $2$ denotes the map $bar 1mapsto bar 2$ (where bar denotes residue class). See the answer to this question.
answered Jan 24 at 18:14
o.h.o.h.
6217
edited Jan 24 at 18:24
answered Jan 24 at 18:14
o.h.o.h.
6217
answered Jan 24 at 18:14
o.h.o.h.
6217
answered Jan 24 at 18:14
o.h.o.h.
6217
6217
add a comment |
add a comment |
1
$begingroup$
Is $Bbb Z_4$ a $Bbb Z_2$-module?
$endgroup$
– Lord Shark the Unknown
Jan 24 at 17:54
$begingroup$
What's wrong with the usual method? 1) Set $M=$ the module you want to resolve. 2) Write $M$ as a quotient of a free module. 3) Identify the kernel $N$ of the quotient map you got in step 2. 4) If $N=0$ stop, you are done. Otherwise, set $M=N$ and go back to step 2.
$endgroup$
– Jyrki Lahtonen
Jan 24 at 18:30