Question

Faithful module is infinitely dimensional as a vector space.

score 106 · Answer 1 · 2026-04-14 22:28:04

106

Views

Faithful module is infinitely dimensional as a vector space.

Published on 14 Apr 2026 - 22:28

score 86 · Answer 2 · 2026-04-11 16:58:11

86

Views

Does there exist a module structure over $\mathbb{C}^2$ as a $\mathbb{C}[x]$-module?

Published on 11 Apr 2026 - 16:58

score 78 · Answer 3 · 2026-04-15 10:40:18

78

Views

$M$ is a faithful $A$-module.

Published on 15 Apr 2026 - 10:40

score 81 · Answer 4 · 2026-04-15 18:52:06

81

Views

If $M\bigoplus N $ submodule $A\bigoplus B$ does it imply either $M$ submodule $A$ or $M$ submodule $ B$?

Published on 15 Apr 2026 - 18:52

score 42 · Answer 5 · 2026-04-15 07:20:01

42

Views

$I$ is a two sided ideal in $A$, $L$ and $M$ are $A$-modules such that $L \subset M$. If $l\in L$ and $l\in MI$ then $l \in LI$?

Published on 15 Apr 2026 - 7:20

score 427 · Answer 6 · 2026-04-15 21:57:41

427

Views

A short exact sequence + exact sequence of opposite direction = split?

Published on 15 Apr 2026 - 21:57

score 368 · Answer 7 · 2026-04-14 02:18:39

368

Views

Annihilators and exact sequence

Published on 14 Apr 2026 - 2:18

score 151 · Answer 8 · 2026-04-13 04:27:00

151

Views

Reference Request: Replacement for Anderson and Fuller

Published on 13 Apr 2026 - 4:27

score 86 · Answer 9 · 2026-04-12 01:46:12

86

Views

Property of free modules.

Published on 12 Apr 2026 - 1:46

score 237 · Answer 10 · 2026-04-14 04:30:28

237

Views

tensor product of polynomial algebra

Published on 14 Apr 2026 - 4:30

score 1.2k · Answer 11 · 2026-04-13 17:12:25

1.2k

Views

Exact functors preserve free modules?

Published on 13 Apr 2026 - 17:12

score 2.4k · Answer 12 · 2026-03-26 17:29:45

2.4k

Views

$\mathbb{Q}$ is a flat $\mathbb{Z}$-module

Published on 26 Mar 2026 - 17:29

score 198 · Answer 13 · 2026-04-14 11:43:16

198

Views

A basic isomorphism of modules (useful for Corollary 2.7 of Atiyah and MacDonald).

Published on 14 Apr 2026 - 11:43

score 84 · Answer 14 · 2026-04-12 07:03:49

84

Views

Is there a natural link between symmetric polynomials and symmetric algebra?

Published on 12 Apr 2026 - 7:03

score 66 · Answer 15 · 2026-04-16 11:45:45

66

Views

If $A \times B$ is the direct product of two rings, must $A$ necessarily be a projective $A \times B$-module?

Published on 16 Apr 2026 - 11:45

List Question

Faithful module is infinitely dimensional as a vector space.

Does there exist a module structure over $\mathbb{C}^2$ as a $\mathbb{C}[x]$-module?

$M$ is a faithful $A$-module.

If $M\bigoplus N $ submodule $A\bigoplus B$ does it imply either $M$ submodule $A$ or $M$ submodule $ B$?

$I$ is a two sided ideal in $A$, $L$ and $M$ are $A$-modules such that $L \subset M$. If $l\in L$ and $l\in MI$ then $l \in LI$?

A short exact sequence + exact sequence of opposite direction = split?

Annihilators and exact sequence

Reference Request: Replacement for Anderson and Fuller

Property of free modules.

tensor product of polynomial algebra

Exact functors preserve free modules?

$\mathbb{Q}$ is a flat $\mathbb{Z}$-module

A basic isomorphism of modules (useful for Corollary 2.7 of Atiyah and MacDonald).

Is there a natural link between symmetric polynomials and symmetric algebra?

If $A \times B$ is the direct product of two rings, must $A$ necessarily be a projective $A \times B$-module?

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