Question

Is the $F [X]$ module $V$ finitely generated?

score 587 · Answer 1 · 2026-03-25 06:24:29

587

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Is the $F [X]$ module $V$ finitely generated?

Published on 25 Mar 2026 - 6:24

score 121 · Answer 2 · 2026-03-20 09:30:04

121

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Localization of Modules over Dedekind domains

Published on 20 Mar 2026 - 9:30

score 75 · Answer 3 · 2026-03-25 18:08:25

75

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Let $A$ an $R$-ideal, $M$ a submodule generated by $n$ elements, $x \in R$ with $xM \subset AM$. Show that $(x^n+y)M = 0$ for some $y \in A$

Published on 25 Mar 2026 - 18:08

score 659 · Answer 4 · 2018-03-18 07:05:46

659

Views

Smith normal form of a given matrix

Published on 18 Mar 2018 - 7:05

score 92 · Answer 5 · 2026-03-25 19:07:13

92

Views

How to show $\frac{M_1 \oplus M´}{M_1} \simeq \frac{N_1 \oplus N´}{N_1} $ if we know $M´ \simeq N´$?

Published on 25 Mar 2026 - 19:07

score 280 · Answer 6 · 2026-03-25 17:24:44

280

Views

On the annihilator of a certain quotient module

Published on 25 Mar 2026 - 17:24

score 53 · Answer 7 · 2026-03-25 06:22:07

53

Views

On finite generation of $IM$ where $M$ is an $R$-module and $I=Ann_R (M/N)$ , where $N$ is a finitely generated submodule of $M$

Published on 25 Mar 2026 - 6:22

score 428 · Answer 8 · 2018-03-18 23:00:19

428

Views

$M =\mathbb{C}[x]/(x^2)$ is not a free module over $\mathbb{C}[x]$

Published on 18 Mar 2018 - 23:00

score 247 · Answer 9 · 2018-03-19 01:12:31

247

Views

Suppose $I\oplus K$ is a free module, then "$KI\subseteq K\cap I$"

Published on 19 Mar 2018 - 1:12

score 39 · Answer 10 · 2018-03-19 02:21:10

39

Views

In a module X over R, if $a\in R$ such that $a.x=0$ for all $x\in X$, then $a=0$?

Published on 19 Mar 2018 - 2:21

score 630 · Answer 11 · 2018-03-19 06:16:20

630

Views

Quotient rings (modules) of a bigger ideal is contained in the quotient ring (modules) of a smaller ideal?

Published on 19 Mar 2018 - 6:16

score 53 · Answer 12 · 2026-03-25 06:22:07

53

Views

On finite generation of a submodule $N$ of a finitely generated $R$-module $M$, such that $IM$ is finitely generated, where $I=Ann_R (M/N)$

Published on 25 Mar 2026 - 6:22

score 1k · Answer 13 · 2018-03-19 15:14:45

1k

Views

Equivalent definition of free module

Published on 19 Mar 2018 - 15:14

score 232 · Answer 14 · 2026-03-25 16:01:04

232

Views

On minimum cardinality of generating sets of modules

Published on 25 Mar 2026 - 16:01

score 1.1k · Answer 15 · 2026-03-25 06:18:51

1.1k

Views

Is $\mathbb Q$ finitely generated as a $\mathbb Z$-module?

Published on 25 Mar 2026 - 6:18

List Question

Is the $F [X]$ module $V$ finitely generated?

Localization of Modules over Dedekind domains

Let $A$ an $R$-ideal, $M$ a submodule generated by $n$ elements, $x \in R$ with $xM \subset AM$. Show that $(x^n+y)M = 0$ for some $y \in A$

Smith normal form of a given matrix

How to show $\frac{M_1 \oplus M´}{M_1} \simeq \frac{N_1 \oplus N´}{N_1} $ if we know $M´ \simeq N´$?

On the annihilator of a certain quotient module

On finite generation of $IM$ where $M$ is an $R$-module and $I=Ann_R (M/N)$ , where $N$ is a finitely generated submodule of $M$

$M =\mathbb{C}[x]/(x^2)$ is not a free module over $\mathbb{C}[x]$

Suppose $I\oplus K$ is a free module, then "$KI\subseteq K\cap I$"

In a module X over R, if $a\in R$ such that $a.x=0$ for all $x\in X$, then $a=0$?

Quotient rings (modules) of a bigger ideal is contained in the quotient ring (modules) of a smaller ideal?

On finite generation of a submodule $N$ of a finitely generated $R$-module $M$, such that $IM$ is finitely generated, where $I=Ann_R (M/N)$

Equivalent definition of free module

On minimum cardinality of generating sets of modules

Is $\mathbb Q$ finitely generated as a $\mathbb Z$-module?

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