Question

Why $\mathbb{Z}_p$ over $\mathbb{Z}_{p^2}$ cannot be free?

score 79 · Answer 1 · 2026-04-09 13:34:12

79

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Why $\mathbb{Z}_p$ over $\mathbb{Z}_{p^2}$ cannot be free?

Published on 09 Apr 2026 - 13:34

score 2.2k · Answer 2 · 2026-04-13 11:18:48

2.2k

Views

Modules over Group algebra / representations example

Published on 13 Apr 2026 - 11:18

score 196 · Answer 3 · 2016-10-09 19:33:14

196

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Exercise 2.17 in Miles Reid's Commutative Algebra

Published on 09 Oct 2016 - 19:33

score 96 · Answer 4 · 2026-04-14 04:57:25

96

Views

Given a short exact sequence, is the following true?

Published on 14 Apr 2026 - 4:57

score 1.2k · Answer 5 · 2026-04-14 19:57:42

1.2k

Views

Rank of Free Module over a Noncommutative Ring

Published on 14 Apr 2026 - 19:57

score 74 · Answer 6 · 2016-10-10 19:01:45

74

Views

Is $\text{Hom}(A,X)+\text{Hom}(A,Y)\to\text{Hom}(A,X+Y)$ always surjective?

Published on 10 Oct 2016 - 19:01

score 169 · Answer 7 · 2016-10-11 03:58:03

169

Views

Show that a finite abelian group M admits a basis as a Z-module if and only if M = {0}

Published on 11 Oct 2016 - 3:58

score 138 · Answer 8 · 2026-03-26 02:47:53

138

Views

$M$ be a finitely gnerated module with a submodule $N$ such that $M/N$ is free , then is $N$ finitely generated?

Published on 26 Mar 2026 - 2:47

score 1.7k · Answer 9 · 2026-03-26 19:11:14

1.7k

Views

Direct product of injective modules is injective: stucked in proof

Published on 26 Mar 2026 - 19:11

score 918 · Answer 10 · 2026-04-13 05:05:37

918

Views

Proof of $R$ is semi simple $\iff $ every finitely generated modules over $R$ is semi-simple.

Published on 13 Apr 2026 - 5:05

score 198 · Answer 11 · 2026-04-12 14:11:18

198

Views

$A$ valuation ring $\Rightarrow$ $A$-submodules of Frac$(A)$ totally ordered?

Published on 12 Apr 2026 - 14:11

score 1.1k · Answer 12 · 2016-10-12 13:42:26

1.1k

Views

Show that $F(M)=M_{\mathrm{tor}}$ not exact

Published on 12 Oct 2016 - 13:42

score 27 · Answer 13 · 2026-04-13 10:08:19

27

Views

How to compute $\dim_R(\hom_A(U,V))$?

Published on 13 Apr 2026 - 10:08

score 736 · Answer 14 · 2026-03-27 08:16:48

736

Views

Group cohomology: coinduced modules.

Published on 27 Mar 2026 - 8:16

score 58 · Answer 15 · 2026-04-07 22:05:18

58

Views

A question concerning the Cellular Algebra, which is why $(P\otimes_AC^{\mu\star})\otimes_RC^\mu\cong(\dim P\otimes_AC^{\mu\star})C^\mu$?

Published on 07 Apr 2026 - 22:05

List Question

Why $\mathbb{Z}_p$ over $\mathbb{Z}_{p^2}$ cannot be free?

Modules over Group algebra / representations example

Exercise 2.17 in Miles Reid's Commutative Algebra

Given a short exact sequence, is the following true?

Rank of Free Module over a Noncommutative Ring

Is $\text{Hom}(A,X)+\text{Hom}(A,Y)\to\text{Hom}(A,X+Y)$ always surjective?

Show that a finite abelian group M admits a basis as a Z-module if and only if M = {0}

$M$ be a finitely gnerated module with a submodule $N$ such that $M/N$ is free , then is $N$ finitely generated?

Direct product of injective modules is injective: stucked in proof

Proof of $R$ is semi simple $\iff $ every finitely generated modules over $R$ is semi-simple.

$A$ valuation ring $\Rightarrow$ $A$-submodules of Frac$(A)$ totally ordered?

Show that $F(M)=M_{\mathrm{tor}}$ not exact

How to compute $\dim_R(\hom_A(U,V))$?

Group cohomology: coinduced modules.

A question concerning the Cellular Algebra, which is why $(P\otimes_AC^{\mu\star})\otimes_RC^\mu\cong(\dim P\otimes_AC^{\mu\star})C^\mu$?

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