Question

R-module is semisimple iff every cyclic R-submodule is semisimple

score 455 · Answer 1 · 2026-04-11 19:22:27

455

Views

R-module is semisimple iff every cyclic R-submodule is semisimple

Published on 11 Apr 2026 - 19:22

score 53 · Answer 2 · 2020-04-23 17:00:07

53

Views

Why is this set an ideal in the ring $R$?

Published on 23 Apr 2020 - 17:00

score 124 · Answer 3 · 2026-03-27 14:02:31

124

Views

Subrings of $\mathbb{Q}$ that are not finitely generated.

Published on 27 Mar 2026 - 14:02

score 39 · Answer 4 · 2026-04-08 21:04:32

39

Views

Confusion around definition product of modules

Published on 08 Apr 2026 - 21:04

score 83 · Answer 5 · 2026-03-25 12:16:27

83

Views

Categorical interpretation of modules (over algebras)

Published on 25 Mar 2026 - 12:16

score 282 · Answer 6 · 2026-04-10 02:27:37

282

Views

Equivalence of modules over different rings

Published on 10 Apr 2026 - 2:27

score 58 · Answer 7 · 2026-03-25 09:14:17

58

Views

Why does this equality hold when solving linear congruence?

Published on 25 Mar 2026 - 9:14

score 270 · Answer 8 · 2026-04-05 21:38:27

270

Views

Prove that $\det (AB)=\det A \det B$ when entries of the matrices are in a non-commutative ring $R$

Published on 05 Apr 2026 - 21:38

score 218 · Answer 9 · 2026-04-11 16:19:37

218

Views

Representation theory - determining al irreducible FG-modules of dimension $n$.

Published on 11 Apr 2026 - 16:19

score 41 · Answer 10 · 2026-04-11 18:56:07

41

Views

What is an $A^\text{op}$-module?

Published on 11 Apr 2026 - 18:56

score 110 · Answer 11 · 2026-03-29 14:59:08

110

Views

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

Published on 29 Mar 2026 - 14:59

score 862 · Answer 12 · 2026-03-26 13:57:19

862

Views

Prove that a complex polynomial has $|p(z)| ≥ 1$ with $z ∈ \mathbb{C}$

Published on 26 Mar 2026 - 13:57

score 34 · Answer 13 · 2026-04-11 17:36:32

34

Views

The $\mathbb C \mathbb Z$ module $V$ has no submodule $W_2$ such that $V=W_1 \oplus W_2$

Published on 11 Apr 2026 - 17:36

score 73 · Answer 14 · 2026-03-25 19:51:38

73

Views

Generalisation of $\text{ker}f \bigoplus \text{Im}f \cong M$

Published on 25 Mar 2026 - 19:51

score 341 · Answer 15 · 2026-04-12 02:56:15

341

Views

$R^\mathbb{N}$ is not finitely generated as an $R$-module

Published on 12 Apr 2026 - 2:56

List Question

R-module is semisimple iff every cyclic R-submodule is semisimple

Why is this set an ideal in the ring $R$?

Subrings of $\mathbb{Q}$ that are not finitely generated.

Confusion around definition product of modules

Categorical interpretation of modules (over algebras)

Equivalence of modules over different rings

Why does this equality hold when solving linear congruence?

Prove that $\det (AB)=\det A \det B$ when entries of the matrices are in a non-commutative ring $R$

Representation theory - determining al irreducible FG-modules of dimension $n$.

What is an $A^\text{op}$-module?

If $\mathrm{Ext}^n_R (M,R/\mathrm{rad}(R))=0$ for all $n\geq 1$, then $\mathrm{Ext}^n_R (M,N)=0$ for all $n\geq 1$.

Prove that a complex polynomial has $|p(z)| ≥ 1$ with $z ∈ \mathbb{C}$

The $\mathbb C \mathbb Z$ module $V$ has no submodule $W_2$ such that $V=W_1 \oplus W_2$

Generalisation of $\text{ker}f \bigoplus \text{Im}f \cong M$

$R^\mathbb{N}$ is not finitely generated as an $R$-module

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