Question

Is there any relation between the projective dimension of $_AM$(i.e.left $A$-module $M$) and the projective dimension of $_{A/I}M$?

score 40 · Answer 1 · 2026-04-15 03:24:28

Is there any relation between the projective dimension of $_AM$(i.e.left $A$-module $M$) and the projective dimension of $_{A/I}M$?

score 103 · Answer 2 · 2026-04-14 12:56:15

103

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A relation between an element and an annihilator

Published on 14 Apr 2026 - 12:56

score 219 · Answer 3 · 2026-04-09 04:18:58

219

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Are these statements about the localization of a module true?

Published on 09 Apr 2026 - 4:18

score 102 · Answer 4 · 2026-04-13 05:17:07

102

Views

Is there a $0$ in the Smith Normal Form?

Published on 13 Apr 2026 - 5:17

score 730 · Answer 5 · 2026-04-14 11:21:07

730

Views

Connection between the annihilator and the localization of a module

Published on 14 Apr 2026 - 11:21

score 86 · Answer 6 · 2026-04-14 22:57:59

86

Views

Isomorphism between R[T]-modules produced from restriction of scalars through evaluation maps.

Published on 14 Apr 2026 - 22:57

score 152 · Answer 7 · 2026-04-13 05:57:17

152

Views

Tensor product and linear dependence

Published on 13 Apr 2026 - 5:57

score 1.7k · Answer 8 · 2026-04-13 02:11:32

1.7k

Views

An isomorphism concerned about any finitely generated projective module

Published on 13 Apr 2026 - 2:11

score 1.3k · Answer 9 · 2026-04-07 18:45:23

1.3k

Views

Is it possible to make any abelian group homomorphism into a linear map?

Published on 07 Apr 2026 - 18:45

score 180 · Answer 10 · 2026-04-15 20:02:39

180

Views

Finding all submodules of $K[x]/\langle Q^3\rangle$, $Q$ irreducible

Published on 15 Apr 2026 - 20:02

score 446 · Answer 11 · 2026-03-28 04:53:20

446

Views

Cyclic left $R$-module $Ra$ is projective if and only if $\mathrm{Ann}_R(a)$ is of the form $Re$ for some $e \in R $ with $e^2=e$

Published on 28 Mar 2026 - 4:53

score 70 · Answer 12 · 2026-04-12 22:01:36

70

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$A\in \mathrm{Mat}_n(\mathbb{Z})$ is the matrix representing $f$. Show that if $\mathrm{Coker}(f)$ is finite, then $|\det A|=|\mathrm{Coker}(f)|$.

Published on 12 Apr 2026 - 22:01

score 77 · Answer 13 · 2026-04-10 18:06:02

77

Views

If $R_3$ is a finitely generated $R_2$-module and $R_2$ is a finitely generated free $R_1$-module, can we say that $R_3$ is a free $R_1$-module?

Published on 10 Apr 2026 - 18:06

score 370 · Answer 14 · 2026-04-13 23:43:22

370

Views

Show every submodule of $Z_{p^{\infty}}$ is of the form $(\frac{1}{p^{n}})\mathbb{Z}/\mathbb{Z}$

Published on 13 Apr 2026 - 23:43

score 35 · Answer 15 · 2026-04-15 00:33:28

35

Views

Why $P_i+N$ is stationnary when $P_i$ are submodules of $M$?

Published on 15 Apr 2026 - 0:33

List Question

Is there any relation between the projective dimension of $_AM$(i.e.left $A$-module $M$) and the projective dimension of $_{A/I}M$?

A relation between an element and an annihilator

Are these statements about the localization of a module true?

Is there a $0$ in the Smith Normal Form?

Connection between the annihilator and the localization of a module

Isomorphism between R[T]-modules produced from restriction of scalars through evaluation maps.

Tensor product and linear dependence

An isomorphism concerned about any finitely generated projective module

Is it possible to make any abelian group homomorphism into a linear map?

Finding all submodules of $K[x]/\langle Q^3\rangle$, $Q$ irreducible

Cyclic left $R$-module $Ra$ is projective if and only if $\mathrm{Ann}_R(a)$ is of the form $Re$ for some $e \in R $ with $e^2=e$

$A\in \mathrm{Mat}_n(\mathbb{Z})$ is the matrix representing $f$. Show that if $\mathrm{Coker}(f)$ is finite, then $|\det A|=|\mathrm{Coker}(f)|$.

If $R_3$ is a finitely generated $R_2$-module and $R_2$ is a finitely generated free $R_1$-module, can we say that $R_3$ is a free $R_1$-module?

Show every submodule of $Z_{p^{\infty}}$ is of the form $(\frac{1}{p^{n}})\mathbb{Z}/\mathbb{Z}$

Why $P_i+N$ is stationnary when $P_i$ are submodules of $M$?

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