List questions from modules

Published on 09 Apr 2026 - 11:52

142

Views

Homogeneous components of a semisimple module

Published on 11 Apr 2020 - 14:13

91

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Given a nonconstant $f\in \Bbb C[x]$, condition for every finitely generated indecomposable $\Bbb C[x]/(f)$-module is projective

Published on 28 Mar 2026 - 11:33

258

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Number of submodules of a module with non-isomorphic composition factors

Published on 11 Apr 2026 - 19:52

394

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Let $A$ be a PID, $M$ an injective finitely generated module. Prove that $M = 0$.

Published on 26 Mar 2026 - 14:29

66

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Proving exactness not at the connecting hom in a Snake Lemma subproblem.

Published on 25 Mar 2026 - 6:04

98

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If $R$ is IBN, do we have $K\oplus R^{n}\cong R^n\implies K=0$?

Published on 25 Mar 2026 - 19:51

146

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On the definition of tensor product for modules of commutative and non-commutative rings.

Published on 14 Apr 2020 - 7:23

15

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for $(a,b)=1$, $a^n$ to $a^{n+b-1}$ modulo $b$ is a complete system of residues of $b$ (except for the remainder 0) Is this right?

Published on 14 Apr 2020 - 13:54

35

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Module $\subset$ Field Notation

Published on 11 Apr 2026 - 23:38

40

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Examples of Bilinear Mappings on modules

Published on 15 Apr 2020 - 5:56

342

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Character is algebraic number

Published on 26 Mar 2026 - 7:31

139

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$\rho:P \to M$ a projective cover for $M$ semi-perfect module. Prove $M$ is indecomposable if and only if $P$ is indecomposable.

Published on 27 Mar 2026 - 23:35

48

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Relationship between cardinality of abelian group and ring in module

Published on 11 Apr 2026 - 2:44

54

Views

Is the fibre-product functor $(-)\times_N M$ exact?

Published on 27 Mar 2026 - 10:31

List Question

Two sided Ideals of a simple ring

Homogeneous components of a semisimple module

Given a nonconstant $f\in \Bbb C[x]$, condition for every finitely generated indecomposable $\Bbb C[x]/(f)$-module is projective

Number of submodules of a module with non-isomorphic composition factors

Let $A$ be a PID, $M$ an injective finitely generated module. Prove that $M = 0$.

Proving exactness not at the connecting hom in a Snake Lemma subproblem.

If $R$ is IBN, do we have $K\oplus R^{n}\cong R^n\implies K=0$?

On the definition of tensor product for modules of commutative and non-commutative rings.

for $(a,b)=1$, $a^n$ to $a^{n+b-1}$ modulo $b$ is a complete system of residues of $b$ (except for the remainder 0) Is this right?

Module $\subset$ Field Notation

Examples of Bilinear Mappings on modules

Character is algebraic number

$\rho:P \to M$ a projective cover for $M$ semi-perfect module. Prove $M$ is indecomposable if and only if $P$ is indecomposable.

Relationship between cardinality of abelian group and ring in module

Is the fibre-product functor $(-)\times_N M$ exact?

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