Question

Injective resolution of $K$ as a $K[x]/x^n$-module

score 406 · Answer 1 · 2026-03-26 14:30:25

406

Views

Injective resolution of $K$ as a $K[x]/x^n$-module

Published on 26 Mar 2026 - 14:30

score 698 · Answer 2 · 2026-03-26 17:34:40

698

Views

Is an infinite direct product or sum of non-trivial modules not finitely generated?

Published on 26 Mar 2026 - 17:34

score 73 · Answer 3 · 2020-04-29 20:30:06

73

Views

Let $R$ be a domain and $a,b$ $\in$ $R$, prove $R/Rb$ $\cong_R$ $Ra/Rab$

Published on 29 Apr 2020 - 20:30

score 783 · Answer 4 · 2026-04-12 00:02:48

783

Views

What is internal direct sum or internal direct product in Dummit and Foote?

Published on 12 Apr 2026 - 0:02

score 126 · Answer 5 · 2026-03-25 19:05:05

126

Views

Prove $Ra/Rab$ $\cong_R$ $R/Rb$ , with $R$ a domain and $a,b$ not zero

Published on 25 Mar 2026 - 19:05

score 496 · Answer 6 · 2026-03-25 21:22:12

496

Views

In a free module, must the intersection of two free submodules be a free submodule?

Published on 25 Mar 2026 - 21:22

score 280 · Answer 7 · 2026-04-06 00:49:06

280

Views

Let $D$ be an integral domain which is not field and $Q=\text{Frac}(D)$. Then $Q$ has not a projective cover as $D$-module.

Published on 06 Apr 2026 - 0:49

score 237 · Answer 8 · 2026-03-26 02:45:55

237

Views

$\operatorname{Hom}_B$ of flat modules is flat over $A$?

Published on 26 Mar 2026 - 2:45

score 77 · Answer 9 · 2026-04-11 19:49:10

77

Views

Need help with an operation on finite length $A$-modules and Grothendieck Group

Published on 11 Apr 2026 - 19:49

score 1.1k · Answer 10 · 2026-03-27 11:37:19

1.1k

Views

Short exact sequence and pushout

Published on 27 Mar 2026 - 11:37

score 32 · Answer 11 · 2026-03-25 21:22:50

32

Views

The number of elements in a linear independent set and the basis with a free module over a commutative ring with identity.

Published on 25 Mar 2026 - 21:22

score 623 · Answer 12 · 2020-05-03 15:40:10

623

Views

If $M$ finitely generated as an $R$-module, is $M$ is finitely generated as an $S$-module, and $S$ is finitely generated as an $R$-module?

Published on 03 May 2020 - 15:40

score 163 · Answer 13 · 2026-04-09 08:45:13

163

Views

Composition of finitely presented ring morphisms.

Published on 09 Apr 2026 - 8:45

score 658 · Answer 14 · 2026-04-07 02:21:21

658

Views

A module homomorphism is injective iff the kernel is isomorphic to the trivial module

Published on 07 Apr 2026 - 2:21

score 547 · Answer 15 · 2026-04-11 08:14:18

547

Views

What is a module over an algebra in the category theoretic sense?

Published on 11 Apr 2026 - 8:14

List Question

Injective resolution of $K$ as a $K[x]/x^n$-module

Is an infinite direct product or sum of non-trivial modules not finitely generated?

Let $R$ be a domain and $a,b$ $\in$ $R$, prove $R/Rb$ $\cong_R$ $Ra/Rab$

What is internal direct sum or internal direct product in Dummit and Foote?

Prove $Ra/Rab$ $\cong_R$ $R/Rb$ , with $R$ a domain and $a,b$ not zero

In a free module, must the intersection of two free submodules be a free submodule?

Let $D$ be an integral domain which is not field and $Q=\text{Frac}(D)$. Then $Q$ has not a projective cover as $D$-module.

$\operatorname{Hom}_B$ of flat modules is flat over $A$?

Need help with an operation on finite length $A$-modules and Grothendieck Group

Short exact sequence and pushout

The number of elements in a linear independent set and the basis with a free module over a commutative ring with identity.

If $M$ finitely generated as an $R$-module, is $M$ is finitely generated as an $S$-module, and $S$ is finitely generated as an $R$-module?

Composition of finitely presented ring morphisms.

A module homomorphism is injective iff the kernel is isomorphic to the trivial module

What is a module over an algebra in the category theoretic sense?

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