List questions from modules

Published on 25 Mar 2026 - 5:05

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version of Nakayama's lemma for group rings

Published on 28 Mar 2026 - 20:58

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Ring/Group actions on the definition of $R$-modules and $R$-algebras.

Published on 25 Mar 2026 - 1:18

84

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If $M/N\cong M$, can we conclude that $N=0$?

Published on 21 Nov 2018 - 3:51

90

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What is an appropriate generalization of this module/ring result

Published on 21 Nov 2018 - 15:53

880

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How to show that $\text{Hom}_R(A\times B ,M)\cong \text{Hom}_R(A,M)\times \text{Hom}_R(B,M) $ when $A, B$, and $M$ are $R$-modules?

Published on 21 Nov 2018 - 16:46

38

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is (A+B)/B=A/B true for A, B modules?

Published on 21 Nov 2018 - 19:28

82

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about flat $R$-modules with different conditions

Published on 27 Mar 2026 - 10:24

127

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If $A\cong B$, then $A\otimes C\cong B\otimes C$.

Published on 22 Nov 2018 - 14:48

59

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On showing that $\varphi(N)=(N+K)/K$, for modules $N,K<M$, $\varphi$ natural map.

Published on 22 Nov 2018 - 15:46

252

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A completely reducible module is Artinian if and only if it is Noetherian.

Published on 25 Mar 2026 - 6:10

279

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Finitely generated free module is projective.

Published on 25 Mar 2026 - 5:03

66

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Exact sequence with finite groups: $0 \to A \xrightarrow[]{\alpha} \mathbb{Z}^d \xrightarrow[]{\beta} \mathbb{Z} \xrightarrow[]{\gamma} B \to0$.

Published on 25 Nov 2018 - 16:52

29

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Can I Find A Map from a Module M to the kernel of a map p from M to M?

Published on 25 Nov 2018 - 20:09

226

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Alternative definition on free modules.

Published on 25 Mar 2026 - 5:11

List Question

Tensor product of modules.

version of Nakayama's lemma for group rings

Ring/Group actions on the definition of $R$-modules and $R$-algebras.

If $M/N\cong M$, can we conclude that $N=0$?

What is an appropriate generalization of this module/ring result

How to show that $\text{Hom}_R(A\times B ,M)\cong \text{Hom}_R(A,M)\times \text{Hom}_R(B,M) $ when $A, B$, and $M$ are $R$-modules?

is (A+B)/B=A/B true for A, B modules?

about flat $R$-modules with different conditions

If $A\cong B$, then $A\otimes C\cong B\otimes C$.

On showing that $\varphi(N)=(N+K)/K$, for modules $N,K<M$, $\varphi$ natural map.

A completely reducible module is Artinian if and only if it is Noetherian.

Finitely generated free module is projective.

Exact sequence with finite groups: $0 \to A \xrightarrow[]{\alpha} \mathbb{Z}^d \xrightarrow[]{\beta} \mathbb{Z} \xrightarrow[]{\gamma} B \to0$.

Can I Find A Map from a Module M to the kernel of a map p from M to M?

Alternative definition on free modules.

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