Mixing
Flat Modules are Torsion-free
0
$begingroup$
Can anyone help me prove that a flat module is torsion-free? I’ve tried supposing is isn’t and then get the contradiction that it isn’t flat, but I’m not having any good results. Any suggestion is welcomed. Thanks.
abstract-algebra modules flatness
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
$endgroup$
add a comment |
0
$begingroup$
Can anyone help me prove that a flat module is torsion-free? I’ve tried supposing is isn’t and then get the contradiction that it isn’t flat, but I’m not having any good results. Any suggestion is welcomed. Thanks.
abstract-algebra modules flatness
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
$endgroup$
$begingroup$
Consider, for a regular element $rin R$, the exact sequence $0to Rto Rto R/(r)to 0$
$endgroup$
– Max
Jan 27 at 17:55
$begingroup$
Ok yeah , that is going to be a s.e.s, i thought about doing something similiar but i dont see where i get what i want.
$endgroup$
– Pedro Santos
Jan 27 at 18:52
$begingroup$
Well you have a flat module and a short exact sequence, what can you do with it ?
$endgroup$
– Max
Jan 27 at 19:10
$begingroup$
Get another short exat sequence
$endgroup$
– Pedro Santos
Jan 27 at 19:13
add a comment |
0
0
0
$begingroup$
Can anyone help me prove that a flat module is torsion-free? I’ve tried supposing is isn’t and then get the contradiction that it isn’t flat, but I’m not having any good results. Any suggestion is welcomed. Thanks.
abstract-algebra modules flatness
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
$endgroup$
Can anyone help me prove that a flat module is torsion-free? I’ve tried supposing is isn’t and then get the contradiction that it isn’t flat, but I’m not having any good results. Any suggestion is welcomed. Thanks.
abstract-algebra modules flatness
abstract-algebra modules flatness
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
edited Jan 27 at 17:37
J. W. Tanner
3,8001320
3,8001320
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
asked Jan 27 at 16:41
Pedro SantosPedro Santos
1609
1609
$begingroup$
Consider, for a regular element $rin R$, the exact sequence $0to Rto Rto R/(r)to 0$
$endgroup$
– Max
Jan 27 at 17:55
$begingroup$
Ok yeah , that is going to be a s.e.s, i thought about doing something similiar but i dont see where i get what i want.
$endgroup$
– Pedro Santos
Jan 27 at 18:52
$begingroup$
Well you have a flat module and a short exact sequence, what can you do with it ?
$endgroup$
– Max
Jan 27 at 19:10
$begingroup$
Get another short exat sequence
$endgroup$
– Pedro Santos
Jan 27 at 19:13
add a comment |
$begingroup$
Consider, for a regular element $rin R$, the exact sequence $0to Rto Rto R/(r)to 0$
$endgroup$
– Max
Jan 27 at 17:55
$begingroup$
Ok yeah , that is going to be a s.e.s, i thought about doing something similiar but i dont see where i get what i want.
$endgroup$
– Pedro Santos
Jan 27 at 18:52
$begingroup$
Well you have a flat module and a short exact sequence, what can you do with it ?
$endgroup$
– Max
Jan 27 at 19:10
$begingroup$
Get another short exat sequence
$endgroup$
– Pedro Santos
Jan 27 at 19:13
$begingroup$
Consider, for a regular element $rin R$, the exact sequence $0to Rto Rto R/(r)to 0$
$endgroup$
– Max
Jan 27 at 17:55
$begingroup$
Consider, for a regular element $rin R$, the exact sequence $0to Rto Rto R/(r)to 0$
$endgroup$
– Max
Jan 27 at 17:55
$begingroup$
Ok yeah , that is going to be a s.e.s, i thought about doing something similiar but i dont see where i get what i want.
$endgroup$
– Pedro Santos
Jan 27 at 18:52
$begingroup$
Ok yeah , that is going to be a s.e.s, i thought about doing something similiar but i dont see where i get what i want.
$endgroup$
– Pedro Santos
Jan 27 at 18:52
$begingroup$
Well you have a flat module and a short exact sequence, what can you do with it ?
$endgroup$
– Max
Jan 27 at 19:10
$begingroup$
Well you have a flat module and a short exact sequence, what can you do with it ?
$endgroup$
– Max
Jan 27 at 19:10
$begingroup$
Get another short exat sequence
$endgroup$
– Pedro Santos
Jan 27 at 19:13
$begingroup$
Get another short exat sequence
$endgroup$
– Pedro Santos
Jan 27 at 19:13
add a comment |
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$begingroup$
Consider, for a regular element $rin R$, the exact sequence $0to Rto Rto R/(r)to 0$
$endgroup$
– Max
Jan 27 at 17:55
$begingroup$
Ok yeah , that is going to be a s.e.s, i thought about doing something similiar but i dont see where i get what i want.
$endgroup$
– Pedro Santos
Jan 27 at 18:52
$begingroup$
Well you have a flat module and a short exact sequence, what can you do with it ?
$endgroup$
– Max
Jan 27 at 19:10
$begingroup$
Get another short exat sequence
$endgroup$
– Pedro Santos
Jan 27 at 19:13