Question

Tensorproducts of modules

score 34 · Answer 1 · 2026-03-25 05:59:54

34

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Tensorproducts of modules

Published on 25 Mar 2026 - 5:59

score 51 · Answer 2 · 2019-05-02 15:58:31

51

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Is a submodule of a semisimple module $\bigoplus_{i\in I}X_i$ of the form $\bigoplus_{i\in K}X_i$ for some $K\subseteq I$?

Published on 02 May 2019 - 15:58

score 172 · Answer 3 · 2019-05-02 22:15:35

172

Views

If $p(x)\in F[x]$ have root $r$ show that $x-r$ is a factor of $p(x)$

Published on 02 May 2019 - 22:15

score 130 · Answer 4 · 2019-05-03 09:41:02

130

Views

Intersection of cyclic submodules and ideals

Published on 03 May 2019 - 9:41

score 382 · Answer 5 · 2019-05-03 10:02:27

382

Views

Let $M$ a cyclic $R$-module of order $\alpha$. If $\beta\mid\alpha$ then there is a unique submodule of order $\beta$

Published on 03 May 2019 - 10:02

score 683 · Answer 6 · 2019-05-03 15:11:30

683

Views

The rank of a module agrees with the dimension of its localization

Published on 03 May 2019 - 15:11

score 102 · Answer 7 · 2019-05-04 14:20:56

102

Views

Hereditary torsion theories and preradicals

Published on 04 May 2019 - 14:20

score 53 · Answer 8 · 2019-05-04 17:25:44

If $I\subseteq R$ is a uniserial ideal of $R$ with finite length and $R/I$ is uniserial of finite length, then $R$ is uniserial of finite length

score 334 · Answer 9 · 2019-05-04 22:03:19

334

Views

Isomorphic $\mathbb{C}[X]$-modules

Published on 04 May 2019 - 22:03

score 109 · Answer 10 · 2019-05-05 03:26:36

109

Views

Are the two scalar multiplication on an $R$ module equivalent?

Published on 05 May 2019 - 3:26

score 723 · Answer 11 · 2026-03-25 09:38:43

723

Views

Ideals of Dedekind rings are projective

Published on 25 Mar 2026 - 9:38

score 57 · Answer 12 · 2019-05-05 22:23:30

57

Views

Showing that M is a finitely generated R-module

Published on 05 May 2019 - 22:23

score 120 · Answer 13 · 2026-03-25 04:36:49

120

Views

Show that this mapping between localized modules is an isomorphism

Published on 25 Mar 2026 - 4:36

score 346 · Answer 14 · 2026-03-29 08:35:23

346

Views

Invertible $R$-module, $R$ local ring, $L \cong R$

Published on 29 Mar 2026 - 8:35

score 65 · Answer 15 · 2019-05-06 14:48:33

65

Views

Proof that $\Omega_{S^{-1}B/A}=S^{-1}\Omega_{B/A}$

Published on 06 May 2019 - 14:48

List Question

Tensorproducts of modules

Is a submodule of a semisimple module $\bigoplus_{i\in I}X_i$ of the form $\bigoplus_{i\in K}X_i$ for some $K\subseteq I$?

If $p(x)\in F[x]$ have root $r$ show that $x-r$ is a factor of $p(x)$

Intersection of cyclic submodules and ideals

Let $M$ a cyclic $R$-module of order $\alpha$. If $\beta\mid\alpha$ then there is a unique submodule of order $\beta$

The rank of a module agrees with the dimension of its localization

Hereditary torsion theories and preradicals

If $I\subseteq R$ is a uniserial ideal of $R$ with finite length and $R/I$ is uniserial of finite length, then $R$ is uniserial of finite length

Isomorphic $\mathbb{C}[X]$-modules

Are the two scalar multiplication on an $R$ module equivalent?

Ideals of Dedekind rings are projective

Showing that M is a finitely generated R-module

Show that this mapping between localized modules is an isomorphism

Invertible $R$-module, $R$ local ring, $L \cong R$

Proof that $\Omega_{S^{-1}B/A}=S^{-1}\Omega_{B/A}$

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