List questions from modules

Published on 12 Apr 2026 - 19:27

63

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Morita equivalent about group algebra and representation ring

Published on 27 Apr 2026 - 12:51

81

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Prove that the polynomial ring $R[x]$ is a flat $R$-module.

Published on 26 Mar 2026 - 16:06

65

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Projective module over a commutative ring $R$ becomes free over some ring containing $R$ .

Published on 15 Apr 2026 - 22:23

84

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Proving two modules are free based on their direct sum

Published on 25 Mar 2026 - 20:17

75

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Primary component of a finitely generated module over PID is a direct sum of cyclic modules.

Published on 14 Apr 2026 - 5:09

41

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Motivation behind tensor product construction

Published on 11 Apr 2026 - 5:44

35

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Unclear about the notation $A^n\to M:(1,0,\ldots,0)\to x_1,\ldots,(0,\ldots,0,1)\to x_n$ in Proposition 1.55

Published on 15 Apr 2026 - 23:30

132

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Pure submodule that is a direct summand

Published on 14 Apr 2026 - 15:34

49

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Which one is the right morphism in the following exact sequence: $0\to A^{r-1}\to A^r\to A\to 0$

Published on 13 Apr 2026 - 23:40

115

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How Should I Prove that M is Torsion-free Given that M is Projective?

Published on 15 Apr 2026 - 5:48

58

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If two modules have a common Jordan-Hölder factor, is there a nonzero map between them?

Published on 12 Apr 2026 - 9:53

39

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Meaning of projection onto one factor in $0\to A^{r-1}\to A^r\to A\to 0$

Published on 25 Mar 2026 - 7:46

77

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About a possible other way to define the flat cover of a module.

Published on 12 Apr 2026 - 8:35

101

Views

What is the injective hull of the ring $R=\mathbb{R}[x]/(x^2)$?

Published on 26 Mar 2026 - 20:40

List Question

Is $k$ in $\textit{Ann}_R(x)=p^k R$ fixed?

Morita equivalent about group algebra and representation ring

Prove that the polynomial ring $R[x]$ is a flat $R$-module.

Projective module over a commutative ring $R$ becomes free over some ring containing $R$ .

Proving two modules are free based on their direct sum

Primary component of a finitely generated module over PID is a direct sum of cyclic modules.

Motivation behind tensor product construction

Unclear about the notation $A^n\to M:(1,0,\ldots,0)\to x_1,\ldots,(0,\ldots,0,1)\to x_n$ in Proposition 1.55

Pure submodule that is a direct summand

Which one is the right morphism in the following exact sequence: $0\to A^{r-1}\to A^r\to A\to 0$

How Should I Prove that M is Torsion-free Given that M is Projective?

If two modules have a common Jordan-Hölder factor, is there a nonzero map between them?

Meaning of projection onto one factor in $0\to A^{r-1}\to A^r\to A\to 0$

About a possible other way to define the flat cover of a module.

What is the injective hull of the ring $R=\mathbb{R}[x]/(x^2)$?

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