List questions from modules

Published on 31 Dec 2014 - 15:18

141

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change the matrix when we extend the field

Published on 31 Dec 2014 - 23:23

68

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$M\simeq X\oplus Y$ and $M/X \simeq Y$

Published on 01 Jan 2015 - 17:27

163

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$R$ noetherian, $I$ injective $R$-module $\Rightarrow$ $S^{-1}I$ is injective over $S^{-1}R$

Published on 26 Mar 2026 - 2:45

1.3k

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Defining a sheaf of differential operators

Published on 25 Mar 2026 - 6:19

405

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Annihilator of extension of scalars vs. the extension the annihilatar

Published on 02 Jan 2015 - 18:28

142

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If $M$ is a $R$ Module which has a finite generating system and $T$ is a submodule of $M$, is there a submodule $F$ such that $M=F\oplus T$?

Published on 02 Oct 2019 - 11:39

567

Views

Applications of Jordan-Holder theorem in an abelian category

Published on 03 Apr 2026 - 19:03

98

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Is $\hom(\bigoplus_i V_i, \bigoplus_j W_j) \cong \bigoplus_i \bigoplus_j(V_i,W_j)?$

Published on 03 Oct 2019 - 18:47

898

Views

Show splitting lemma for short exact sequences

Published on 26 Mar 2026 - 17:30

587

Views

Injective module characterisation

Published on 26 Mar 2026 - 2:51

324

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Proof of Baer's criterion: what set to apply Zorn on?

Published on 26 Mar 2026 - 2:46

248

Views

Injective homomorphism of artinian modules is surjective.

Published on 26 Mar 2026 - 17:31

96

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Characterization of flat modules $M$ for which tensoring with $M$ preserves arbitrary intersections

Published on 25 Mar 2026 - 22:10

188

Views

Socle of sum is the sum of socles

Published on 29 Mar 2026 - 4:44

List Question

On the Semisimplicity of a Permutation Module given by a Transitive Group Action

change the matrix when we extend the field

$M\simeq X\oplus Y$ and $M/X \simeq Y$

$R$ noetherian, $I$ injective $R$-module $\Rightarrow$ $S^{-1}I$ is injective over $S^{-1}R$

Defining a sheaf of differential operators

Annihilator of extension of scalars vs. the extension the annihilatar

If $M$ is a $R$ Module which has a finite generating system and $T$ is a submodule of $M$, is there a submodule $F$ such that $M=F\oplus T$?

Applications of Jordan-Holder theorem in an abelian category

Is $\hom(\bigoplus_i V_i, \bigoplus_j W_j) \cong \bigoplus_i \bigoplus_j(V_i,W_j)?$

Show splitting lemma for short exact sequences

Injective module characterisation

Proof of Baer's criterion: what set to apply Zorn on?

Injective homomorphism of artinian modules is surjective.

Characterization of flat modules $M$ for which tensoring with $M$ preserves arbitrary intersections

Socle of sum is the sum of socles

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