Question

How can one express $\mathbb{Q} / \mathbb{Z}$ as a direct sum of $\mathbb{Q}$ and $\mathbb{Z} / p$ for $p$ prime?

score 235 · Answer 1 · 2026-04-12 20:32:56

235

Views

How can one express $\mathbb{Q} / \mathbb{Z}$ as a direct sum of $\mathbb{Q}$ and $\mathbb{Z} / p$ for $p$ prime?

Published on 12 Apr 2026 - 20:32

score 379 · Answer 2 · 2026-04-14 13:29:10

379

Views

The category of finitely generated abelian groups does not have enough injectives

Published on 14 Apr 2026 - 13:29

score 98 · Answer 3 · 2026-04-14 14:41:04

98

Views

Prove that $\varphi$ is an isomorphism.

Published on 14 Apr 2026 - 14:41

score 155 · Answer 4 · 2026-04-14 08:39:53

155

Views

A module $N$ is semisimple $\Longleftrightarrow$ $N$ has no proper essential submodules

Published on 14 Apr 2026 - 8:39

score 234 · Answer 5 · 2026-04-16 07:04:32

234

Views

Prove $F[x]/(x^n)$ is an injective module

Published on 16 Apr 2026 - 7:04

score 192 · Answer 6 · 2026-04-16 12:40:09

192

Views

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Published on 16 Apr 2026 - 12:40

score 58 · Answer 7 · 2026-04-14 00:32:32

58

Views

Is $\operatorname{Quot}(R)/R$ an injective $R$-Module?

Published on 14 Apr 2026 - 0:32

score 82 · Answer 8 · 2026-04-15 14:04:44

82

Views

$R$ is a noetherian ring and $I$ is an injective $R$-module. Let $J\subset R$ be an ideal. Then $I_1=\{x\in I\mid\exists n,J^nx=0\}$ is injective.

Published on 15 Apr 2026 - 14:04

score 744 · Answer 9 · 2026-04-13 01:54:30

744

Views

Over an integral domain is a module injective iff it is divisible?

Published on 13 Apr 2026 - 1:54

score 376 · Answer 10 · 2026-04-12 01:42:01

376

Views

Projective and injective objects

Published on 12 Apr 2026 - 1:42

score 213 · Answer 11 · 2026-04-13 16:48:52

213

Views

Projective and Injective Modules

Published on 13 Apr 2026 - 16:48

score 142 · Answer 12 · 2026-04-11 08:38:44

142

Views

Is the following abelian group injective?

Published on 11 Apr 2026 - 8:38

score 138 · Answer 13 · 2026-04-16 14:17:39

138

Views

If a left ideal of R is a direct summand of R, is I an injective R-module?

Published on 16 Apr 2026 - 14:17

score 114 · Answer 14 · 2026-04-16 15:49:05

114

Views

If a left ideal I of R is an injective R-module then I is a projective R-module. Is the converse true?

Published on 16 Apr 2026 - 15:49

score 517 · Answer 15 · 2026-04-14 18:13:01

517

Views

Is there an analogue of Bass-Papp theorem for Projective modules?

Published on 14 Apr 2026 - 18:13

List Question

How can one express $\mathbb{Q} / \mathbb{Z}$ as a direct sum of $\mathbb{Q}$ and $\mathbb{Z} / p$ for $p$ prime?

The category of finitely generated abelian groups does not have enough injectives

Prove that $\varphi$ is an isomorphism.

A module $N$ is semisimple $\Longleftrightarrow$ $N$ has no proper essential submodules

Prove $F[x]/(x^n)$ is an injective module

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Is $\operatorname{Quot}(R)/R$ an injective $R$-Module?

$R$ is a noetherian ring and $I$ is an injective $R$-module. Let $J\subset R$ be an ideal. Then $I_1=\{x\in I\mid\exists n,J^nx=0\}$ is injective.

Over an integral domain is a module injective iff it is divisible?

Projective and injective objects

Projective and Injective Modules

Is the following abelian group injective?

If a left ideal of R is a direct summand of R, is I an injective R-module?

If a left ideal I of R is an injective R-module then I is a projective R-module. Is the converse true?

Is there an analogue of Bass-Papp theorem for Projective modules?

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