List questions from modules

Published on 15 Apr 2026 - 12:00

144

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Show that any nonzero free $F[x]$-module $V$ is an infinite dimensional vector space over $F$.

Published on 17 Apr 2026 - 12:26

61

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Comparing Ranks of Free Modules

Published on 13 Apr 2026 - 13:36

47

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Finiteness of the Injective Hull

Published on 26 Mar 2026 - 17:31

39

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Terminology for a certain image of an action

Published on 14 Apr 2026 - 10:44

41

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Showing $\operatorname{Mod}(R,C)$ is $k$-abelian when $C$ is and related.

Published on 09 Apr 2026 - 8:09

73

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Automorphisms of matrix algebras and Picard Group

Published on 25 Mar 2026 - 11:13

94

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$R$-modules satisfying $M^{\otimes n}\simeq R$ but not $M^n\simeq R^n$

Published on 25 Mar 2026 - 9:29

16

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Any CS summand-square-free module is square-free

Published on 15 Apr 2026 - 10:51

115

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Let $M$ be an $R$-module for an integral domain $R$, and $N$ a submodule of $M$. Give an example where $Ann(M/N)Ann(N)\neq Ann(M)$.

Published on 16 Apr 2026 - 14:50

85

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Free module and exact sequences

Published on 15 Apr 2026 - 11:40

48

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What exactly is the relationship between associated primes and the radical ideal?

Published on 25 Mar 2026 - 17:39

202

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Help understanding proof involving Schur's Lemma.

Published on 09 Apr 2026 - 12:34

92

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Exactness of group invariants

Published on 10 Apr 2026 - 22:49

130

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Proving that any irreducible complex representation of an abelian group is 1-dimensional.

Published on 15 Apr 2026 - 19:09

List Question

relation between finite generating set and ascending chain condition

Show that any nonzero free $F[x]$-module $V$ is an infinite dimensional vector space over $F$.

Comparing Ranks of Free Modules

Finiteness of the Injective Hull

Terminology for a certain image of an action

Showing $\operatorname{Mod}(R,C)$ is $k$-abelian when $C$ is and related.

Automorphisms of matrix algebras and Picard Group

$R$-modules satisfying $M^{\otimes n}\simeq R$ but not $M^n\simeq R^n$

Any CS summand-square-free module is square-free

Let $M$ be an $R$-module for an integral domain $R$, and $N$ a submodule of $M$. Give an example where $Ann(M/N)Ann(N)\neq Ann(M)$.

Free module and exact sequences

What exactly is the relationship between associated primes and the radical ideal?

Help understanding proof involving Schur's Lemma.

Exactness of group invariants

Proving that any irreducible complex representation of an abelian group is 1-dimensional.

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