Question

Definition of semisimple modules

score 180 · Answer 1 · 2026-04-10 21:19:08

180

Views

Definition of semisimple modules

Published on 10 Apr 2026 - 21:19

score 214 · Answer 2 · 2026-04-15 13:13:00

214

Views

A module J that is a direct summand of every module containing J

Published on 15 Apr 2026 - 13:13

score 102 · Answer 3 · 2026-04-16 08:54:57

102

Views

$R$ is a domain such that for $x,y \in R$, $(x)\subseteq (y)$ or $(y)\subseteq (x)$ . Is every f.g. torsion free module over $R$ free?

Published on 16 Apr 2026 - 8:54

score 764 · Answer 4 · 2026-04-14 20:51:54

764

Views

Every non-finitely generated module has a minimal generating set.

Published on 14 Apr 2026 - 20:51

score 91 · Answer 5 · 2026-04-11 02:23:44

91

Views

What is a general kind of tensor product of things with a commutative operation?

Published on 11 Apr 2026 - 2:23

score 168 · Answer 6 · 2026-04-13 22:04:03

168

Views

Showing a particular quotient is noetherian/artinian

Published on 13 Apr 2026 - 22:04

score 32 · Answer 7 · 2026-04-16 04:26:13

32

Views

About group algebras. Are $R(G_1\times G_2)$, $(RG_1)G_2$ isomorphic?

Published on 16 Apr 2026 - 4:26

score 99 · Answer 8 · 2026-04-15 15:12:50

99

Views

$\ker(\alpha)$ is a direct summand of the pullback

Published on 15 Apr 2026 - 15:12

score 98 · Answer 9 · 2026-04-14 16:52:10

98

Views

existence of an exact complex

Published on 14 Apr 2026 - 16:52

score 69 · Answer 10 · 2026-04-15 17:25:34

69

Views

Constructing two non-isomorphic irreducible $\mathbb Q[x]$ modules with the underlying abelian group $\mathbb Q\times\mathbb Q$.

Published on 15 Apr 2026 - 17:25

score 146 · Answer 11 · 2026-04-16 10:24:30

146

Views

Show that $\mathrm{Hom}_R(K,M\oplus N)\cong \mathrm{Hom}_R(K,M)\oplus \mathrm{Hom}_R(K,N).$

Published on 16 Apr 2026 - 10:24

score 768 · Answer 12 · 2026-04-15 10:38:50

768

Views

Localization of a module at a prime ideal and local behavior.

Published on 15 Apr 2026 - 10:38

score 1.2k · Answer 13 · 2026-04-17 00:06:30

1.2k

Views

Let R be a ring viewed as an R-module over itself, and prove that $Hom_{R-Mod}(R,M) \cong M$ as modules.

Published on 17 Apr 2026 - 0:06

score 355 · Answer 14 · 2026-04-10 03:44:17

355

Views

Artinian ring and injective endomorphism which is not surjective

Published on 10 Apr 2026 - 3:44

score 66 · Answer 15 · 2026-04-09 18:41:07

66

Views

Natural Isomorphism of Functions

Published on 09 Apr 2026 - 18:41

List Question

Definition of semisimple modules

A module J that is a direct summand of every module containing J

$R$ is a domain such that for $x,y \in R$, $(x)\subseteq (y)$ or $(y)\subseteq (x)$ . Is every f.g. torsion free module over $R$ free?

Every non-finitely generated module has a minimal generating set.

What is a general kind of tensor product of things with a commutative operation?

Showing a particular quotient is noetherian/artinian

About group algebras. Are $R(G_1\times G_2)$, $(RG_1)G_2$ isomorphic?

$\ker(\alpha)$ is a direct summand of the pullback

existence of an exact complex

Constructing two non-isomorphic irreducible $\mathbb Q[x]$ modules with the underlying abelian group $\mathbb Q\times\mathbb Q$.

Show that $\mathrm{Hom}_R(K,M\oplus N)\cong \mathrm{Hom}_R(K,M)\oplus \mathrm{Hom}_R(K,N).$

Localization of a module at a prime ideal and local behavior.

Let R be a ring viewed as an R-module over itself, and prove that $Hom_{R-Mod}(R,M) \cong M$ as modules.

Artinian ring and injective endomorphism which is not surjective

Natural Isomorphism of Functions

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