List questions from modules

Published on 09 Apr 2026 - 1:46

40

Views

If $Ext_A^n(M,N) \ne 0$, then $Ext_A^n(M,N') \ne 0$, for every indecomposable summand N' of N?

Published on 16 Apr 2026 - 6:57

666

Views

Why is this Hilbert's Syzygy theorem?

Published on 14 Apr 2026 - 11:30

606

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Proving that a module can be decomposed as a direct sum of submodules

Published on 14 Apr 2026 - 9:34

293

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Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$

Published on 15 Apr 2026 - 14:11

1.2k

Views

Proving that two quotient modules are isomorphic

Published on 14 Apr 2026 - 8:09

91

Views

Properties of module length

Published on 08 Apr 2026 - 21:09

349

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Vector spaces and endomorphisms as $K[X]$-Modules

Published on 16 Apr 2026 - 15:12

45

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about homomorphismes of modules

Published on 10 Apr 2026 - 18:15

883

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Specific examples of submodules.

Published on 14 Apr 2026 - 6:16

1.1k

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On semisimple rings

Published on 26 Apr 2026 - 13:41

258

Views

$\text{Coker}(f),\text{Coker}(g)$ projective modules $\Rightarrow$ $\text{Coker}(gf)$ projective

Published on 15 Apr 2026 - 15:09

4.7k

Views

Different definitions of submodule

Published on 11 Apr 2026 - 3:45

255

Views

Over a Bezout domain $R$, show every finitely generated submodule of $R^n$ is free

Published on 16 Apr 2026 - 9:45

76

Views

$M\simeq D$ and $N\simeq D$ then $M\oplus N\simeq D\oplus D$?

Published on 17 Apr 2026 - 0:19

List Question

Intuitive explanation of Four Lemma

If $Ext_A^n(M,N) \ne 0$, then $Ext_A^n(M,N') \ne 0$, for every indecomposable summand N' of N?

Why is this Hilbert's Syzygy theorem?

Proving that a module can be decomposed as a direct sum of submodules

Prove that $Ker(g \otimes k)= Im(f \otimes 1_{N}) + Im (1_{M} \otimes h)$

Proving that two quotient modules are isomorphic

Properties of module length

Vector spaces and endomorphisms as $K[X]$-Modules

about homomorphismes of modules

Specific examples of submodules.

On semisimple rings

$\text{Coker}(f),\text{Coker}(g)$ projective modules $\Rightarrow$ $\text{Coker}(gf)$ projective

Different definitions of submodule

Over a Bezout domain $R$, show every finitely generated submodule of $R^n$ is free

$M\simeq D$ and $N\simeq D$ then $M\oplus N\simeq D\oplus D$?

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