List questions from modules

Published on 12 Apr 2026 - 16:34

724

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Minimum number of generators of a module and its 'local dimension'

Published on 14 Apr 2026 - 13:09

119

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Reflexive implies short exact sequence

Published on 15 Apr 2026 - 0:14

173

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Commutative Local Rings and Jacobson Radical

Published on 16 Apr 2026 - 20:42

34

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Counting some kind of modules in a number field

Published on 13 Apr 2026 - 2:48

56

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If $f^m(x_1,...,x_n)=0$ why $f(x_1,...,x_n)=0$?

Published on 15 Apr 2026 - 20:09

764

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proof of Nakayama's lemma

Published on 12 Apr 2026 - 12:27

41

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Let $N \to M$ be an abelian subgroup. Use surjectivity of $R\to S$ to show that $N$ is an $S$-submodule if and only if it is an $R$-submodule.

Published on 14 Apr 2026 - 18:23

91

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$RG\otimes_{RP}RL\simeq RGe_U$, when $P=LU$ is a parabolic subgroup of $G$?

Published on 16 Apr 2026 - 11:22

258

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$ρ:Hom_A(M,N)\otimes_A B \rightarrow Hom_B(B\otimes_A M,B\otimes_A N)$, if $M$ is free of finite rank over $A$, then $ρ$ is an isomorphism?

Published on 16 Apr 2026 - 9:20

309

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If $M$ and $N/M$ are finitely generated, then so is $N$.

Published on 16 Apr 2026 - 4:29

635

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How can I prove that $\mathbb Z[x]/(1+x^2)\mathbb Z[x]$ is a free module with basis $\{1,\bar x\}$?

Published on 14 Apr 2026 - 23:44

158

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When is the socle small?

Published on 11 Apr 2026 - 16:12

32

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How to solve $x^2 - 1$ in ring $\mathbb{Z}/700\mathbb{Z}$

Published on 12 Apr 2026 - 2:39

207

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Proof of Noether Normalization for finite field

Published on 09 Apr 2026 - 16:27

List Question

On the basis of a free module over a PID

Minimum number of generators of a module and its 'local dimension'

Reflexive implies short exact sequence

Commutative Local Rings and Jacobson Radical

Counting some kind of modules in a number field

If $f^m(x_1,...,x_n)=0$ why $f(x_1,...,x_n)=0$?

proof of Nakayama's lemma

Let $N \to M$ be an abelian subgroup. Use surjectivity of $R\to S$ to show that $N$ is an $S$-submodule if and only if it is an $R$-submodule.

$RG\otimes_{RP}RL\simeq RGe_U$, when $P=LU$ is a parabolic subgroup of $G$?

$ρ:Hom_A(M,N)\otimes_A B \rightarrow Hom_B(B\otimes_A M,B\otimes_A N)$, if $M$ is free of finite rank over $A$, then $ρ$ is an isomorphism?

If $M$ and $N/M$ are finitely generated, then so is $N$.

How can I prove that $\mathbb Z[x]/(1+x^2)\mathbb Z[x]$ is a free module with basis $\{1,\bar x\}$?

When is the socle small?

How to solve $x^2 - 1$ in ring $\mathbb{Z}/700\mathbb{Z}$

Proof of Noether Normalization for finite field

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