Question

How to show $\mathrm{Hom}_\mathsf{Ab}(\mathbb Z/a\mathbb Z,\mathbb Z/b\mathbb Z) \cong \mathbb Z/(a,b)\mathbb Z$?

score 90 · Answer 1 · 2026-03-27 07:14:55

90

Views

How to show $\mathrm{Hom}_\mathsf{Ab}(\mathbb Z/a\mathbb Z,\mathbb Z/b\mathbb Z) \cong \mathbb Z/(a,b)\mathbb Z$?

Published on 27 Mar 2026 - 7:14

score 469 · Answer 2 · 2019-06-22 21:58:11

469

Views

Saturation of a submodule

Published on 22 Jun 2019 - 21:58

score 132 · Answer 3 · 2026-03-25 11:10:07

132

Views

Do flat modules form a reflective subcategory only for semihereditary rings?

Published on 25 Mar 2026 - 11:10

score 45 · Answer 4 · 2026-03-26 03:12:33

45

Views

How do I show that $B \to A \oplus C$ where $b \mapsto (p(b), j(b))$ is surjective?

Published on 26 Mar 2026 - 3:12

score 472 · Answer 5 · 2019-06-24 12:28:59

472

Views

What is interesting about the support of a module?

Published on 24 Jun 2019 - 12:28

score 154 · Answer 6 · 2026-03-26 06:31:51

154

Views

In proving Splitting Lemma, why does Aluffi show $N \cong M \oplus \ker \psi$ instead of $N \cong M \oplus \mathrm{coker}\varphi$ like Hatcher?

Published on 26 Mar 2026 - 6:31

score 38 · Answer 7 · 2026-03-26 01:02:00

38

Views

Equivalent definitions of module homomorphism

Published on 26 Mar 2026 - 1:02

score 150 · Answer 8 · 2019-06-25 08:36:47

150

Views

co-semisimple module and its radical

Published on 25 Jun 2019 - 8:36

score 264 · Answer 9 · 2026-03-27 10:46:20

264

Views

Conditions to Make $\text{Hom}(M, N) \cong M^* \otimes N$.

Published on 27 Mar 2026 - 10:46

score 132 · Answer 10 · 2026-03-25 15:38:18

132

Views

Atiyah Macdonald Exercise 6.2

Published on 25 Mar 2026 - 15:38

score 150 · Answer 11 · 2026-03-27 02:02:41

150

Views

Short exact sequence of finite Abelian groups with the last group having odd order.

Published on 27 Mar 2026 - 2:02

score 280 · Answer 12 · 2026-02-23 02:12:59

280

Views

Socle of representations of Klein Four group over $\mathbb{F}_2$

Published on 23 Feb 2026 - 2:12

score 1.3k · Answer 13 · 2026-03-25 11:53:24

1.3k

Views

Why is every vector space free, but not every module?

Published on 25 Mar 2026 - 11:53

score 212 · Answer 14 · 2019-06-27 16:56:47

212

Views

Generating set for Polynomial rings

Published on 27 Jun 2019 - 16:56

score 556 · Answer 15 · 2026-03-25 21:12:45

556

Views

Direct Sum In modules

Published on 25 Mar 2026 - 21:12

List Question

How to show $\mathrm{Hom}_\mathsf{Ab}(\mathbb Z/a\mathbb Z,\mathbb Z/b\mathbb Z) \cong \mathbb Z/(a,b)\mathbb Z$?

Saturation of a submodule

Do flat modules form a reflective subcategory only for semihereditary rings?

How do I show that $B \to A \oplus C$ where $b \mapsto (p(b), j(b))$ is surjective?

What is interesting about the support of a module?

In proving Splitting Lemma, why does Aluffi show $N \cong M \oplus \ker \psi$ instead of $N \cong M \oplus \mathrm{coker}\varphi$ like Hatcher?

Equivalent definitions of module homomorphism

co-semisimple module and its radical

Conditions to Make $\text{Hom}(M, N) \cong M^* \otimes N$.

Atiyah Macdonald Exercise 6.2

Short exact sequence of finite Abelian groups with the last group having odd order.

Socle of representations of Klein Four group over $\mathbb{F}_2$

Why is every vector space free, but not every module?

Generating set for Polynomial rings

Direct Sum In modules

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