Question

Proving that $\operatorname{Hom}(\mathbb{Z}/m\mathbb{Z},\mathbb{Z}/n\mathbb{Z}) \cong \mathbb{Z}/\gcd(m,n)\mathbb{Z},$

score 165 · Answer 1 · 2018-12-04 04:28:21

165

Views

Proving that $\operatorname{Hom}(\mathbb{Z}/m\mathbb{Z},\mathbb{Z}/n\mathbb{Z}) \cong \mathbb{Z}/\gcd(m,n)\mathbb{Z},$

Published on 04 Dec 2018 - 4:28

score 120 · Answer 2 · 2018-12-05 06:58:58

120

Views

If $I$ is an ideal of a ring $R$, then for any $a\in R$, is there a difference between $(R/I)a$ and $Ra/I$?

Published on 05 Dec 2018 - 6:58

score 128 · Answer 3 · 2026-03-27 01:13:30

128

Views

If possible, construct a simple module that is not projective.

Published on 27 Mar 2026 - 1:13

score 44 · Answer 4 · 2018-12-05 19:21:15

44

Views

Surjective module homomorphism? $0$ module homomorphism?

Published on 05 Dec 2018 - 19:21

score 3.4k · Answer 5 · 2018-12-05 23:13:30

3.4k

Views

What do brackets mean for mod operation?

Published on 05 Dec 2018 - 23:13

score 362 · Answer 6 · 2018-12-05 23:25:57

362

Views

What do "projections" out of tensor products look like?

Published on 05 Dec 2018 - 23:25

score 32 · Answer 7 · 2018-12-06 10:50:29

32

Views

prove the next algebras isomorphism

Published on 06 Dec 2018 - 10:50

score 46 · Answer 8 · 2018-12-08 09:20:24

46

Views

How to take an absolute value or modulus of z?

Published on 08 Dec 2018 - 9:20

score 59 · Answer 9 · 2026-03-29 03:21:45

59

Views

Is $R$ an algebra or not?

Published on 29 Mar 2026 - 3:21

score 336 · Answer 10 · 2018-12-10 03:11:49

336

Views

The matrix corresponds to a homomorphism $\mathbb{Z^2} → \mathbb{Z^3}$

Published on 10 Dec 2018 - 3:11

score 47 · Answer 11 · 2026-03-25 18:45:54

47

Views

Does $\operatorname{length}(M/xM) \leq \operatorname{rank}(M) \cdot \operatorname{length}(R/(x))$ hold over non-integral rings $R$?

Published on 25 Mar 2026 - 18:45

score 71 · Answer 12 · 2018-12-11 03:07:40

71

Views

Interpretation of the cardinality of cokernel

Published on 11 Dec 2018 - 3:07

score 756 · Answer 13 · 2018-12-13 14:30:53

756

Views

In $R$-Mod Category, example for $B\cong A \oplus C \nRightarrow 0 \to A \to B \to C \to0$ splits.

Published on 13 Dec 2018 - 14:30

score 85 · Answer 14 · 2026-03-21 23:41:17

85

Views

Reduced rings and simple modules

Published on 21 Mar 2026 - 23:41

score 1.2k · Answer 15 · 2026-03-29 03:02:35

1.2k

Views

About the definition of coinduction of a module

Published on 29 Mar 2026 - 3:02

List Question

Proving that $\operatorname{Hom}(\mathbb{Z}/m\mathbb{Z},\mathbb{Z}/n\mathbb{Z}) \cong \mathbb{Z}/\gcd(m,n)\mathbb{Z},$

If $I$ is an ideal of a ring $R$, then for any $a\in R$, is there a difference between $(R/I)a$ and $Ra/I$?

If possible, construct a simple module that is not projective.

Surjective module homomorphism? $0$ module homomorphism?

What do brackets mean for mod operation?

What do "projections" out of tensor products look like?

prove the next algebras isomorphism

How to take an absolute value or modulus of z?

Is $R$ an algebra or not?

The matrix corresponds to a homomorphism $\mathbb{Z^2} → \mathbb{Z^3}$

Does $\operatorname{length}(M/xM) \leq \operatorname{rank}(M) \cdot \operatorname{length}(R/(x))$ hold over non-integral rings $R$?

Interpretation of the cardinality of cokernel

In $R$-Mod Category, example for $B\cong A \oplus C \nRightarrow 0 \to A \to B \to C \to0$ splits.

Reduced rings and simple modules

About the definition of coinduction of a module

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