Question

direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules

score 570 · Answer 1 · 2026-03-22 09:54:24

570

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direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules

Published on 22 Mar 2026 - 9:54

score 146 · Answer 2 · 2026-03-24 22:39:06

146

Views

injective hull of a ring that is not integral domain

Published on 24 Mar 2026 - 22:39

score 301 · Answer 3 · 2026-03-23 11:21:49

301

Views

Decomposition of injective modules over polynomial rings

Published on 23 Mar 2026 - 11:21

score 181 · Answer 4 · 2026-03-23 11:12:32

181

Views

Problem based on Projective and Injective Module

Published on 23 Mar 2026 - 11:12

score 418 · Answer 5 · 2026-03-22 21:14:34

418

Views

Example of reduced module

Published on 22 Mar 2026 - 21:14

score 107 · Answer 6 · 2026-03-22 21:02:55

107

Views

Injective object in the category of projective systems of $R$-modules.

Published on 22 Mar 2026 - 21:02

score 91 · Answer 7 · 2026-03-23 06:12:38

91

Views

Injective Linear Transformation $K[x]_{\leq 4}\rightarrow V$

Published on 23 Mar 2026 - 6:12

score 420 · Answer 8 · 2026-03-22 18:45:46

420

Views

For $d\mid m$, $\mathbb{Z}/d\mathbb{Z}$ is not an injective $\mathbb{Z}/m\mathbb{Z}$-module when some prime divides $d$ and $\frac{m}{d}$

Published on 22 Mar 2026 - 18:45

score 355 · Answer 9 · 2026-03-22 03:30:27

355

Views

$\mathbb{Q}_{\mathbb{Z}}$ is an injective hull of $\mathbb{Z}$

Published on 22 Mar 2026 - 3:30

score 344 · Answer 10 · 2026-03-22 17:43:37

344

Views

Element in a finitely generated torsion module on a PID with smallest non-zero annihilator

Published on 22 Mar 2026 - 17:43

score 1.1k · Answer 11 · 2026-03-22 22:24:31

1.1k

Views

Let $R$ be a Noetherian Ring, then the category of $R$-modules has enough injectives

Published on 22 Mar 2026 - 22:24

score 767 · Answer 12 · 2026-03-23 21:30:09

767

Views

If $Q$ is injective, then $\text{Hom}_{\mathbb Z}(R, Q)$ is injective.

Published on 23 Mar 2026 - 21:30

score 1.6k · Answer 13 · 2026-03-24 07:22:15

1.6k

Views

Prove that no $\mathbb{Z}$-module is both projective and injective

Published on 24 Mar 2026 - 7:22

score 1k · Answer 14 · 2026-03-22 17:12:39

1k

Views

Quotient of injective module which is not injective

Published on 22 Mar 2026 - 17:12

score 324 · Answer 15 · 2026-03-22 17:52:35

324

Views

Injective module

Published on 22 Mar 2026 - 17:52

List Question

direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules

injective hull of a ring that is not integral domain

Decomposition of injective modules over polynomial rings

Problem based on Projective and Injective Module

Example of reduced module

Injective object in the category of projective systems of $R$-modules.

Injective Linear Transformation $K[x]_{\leq 4}\rightarrow V$

For $d\mid m$, $\mathbb{Z}/d\mathbb{Z}$ is not an injective $\mathbb{Z}/m\mathbb{Z}$-module when some prime divides $d$ and $\frac{m}{d}$

$\mathbb{Q}_{\mathbb{Z}}$ is an injective hull of $\mathbb{Z}$

Element in a finitely generated torsion module on a PID with smallest non-zero annihilator

Let $R$ be a Noetherian Ring, then the category of $R$-modules has enough injectives

If $Q$ is injective, then $\text{Hom}_{\mathbb Z}(R, Q)$ is injective.

Prove that no $\mathbb{Z}$-module is both projective and injective

Quotient of injective module which is not injective

Injective module

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