Question

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

score 590 · Answer 1 · 2026-05-10 13:24:13

590

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

Published on 10 May 2026 - 13:24

score 129 · Answer 2 · 2026-05-07 11:34:08

129

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Localization of Modules over Dedekind domains

Published on 07 May 2026 - 11:34

score 78 · Answer 3 · 2026-05-11 00:34:55

78

Views

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 11 May 2026 - 0:34

score 662 · Answer 4 · 2026-04-15 13:30:04

662

Views

Smith normal form of a given matrix

Published on 15 Apr 2026 - 13:30

score 94 · Answer 5 · 2026-04-15 17:49:30

94

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 15 Apr 2026 - 17:49

score 283 · Answer 6 · 2026-05-10 14:55:48

283

Views

On the annihilator of a certain quotient module

Published on 10 May 2026 - 14:55

score 56 · Answer 7 · 2026-05-10 13:28:09

56

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 10 May 2026 - 13:28

score 431 · Answer 8 · 2026-04-12 04:05:14

431

Views

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

Published on 12 Apr 2026 - 4:05

score 250 · Answer 9 · 2026-04-13 20:52:59

250

Views

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

Published on 13 Apr 2026 - 20:52

score 42 · Answer 10 · 2026-04-14 04:31:04

42

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 14 Apr 2026 - 4:31

score 633 · Answer 11 · 2026-04-12 22:41:45

633

Views

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

Published on 12 Apr 2026 - 22:41

score 56 · Answer 12 · 2026-05-10 13:28:09

56

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 10 May 2026 - 13:28

score 1k · Answer 13 · 2026-04-14 20:00:52

1k

Views

Equivalent definition of free module

Published on 14 Apr 2026 - 20:00

score 235 · Answer 14 · 2026-05-10 17:19:39

235

Views

On minimum cardinality of generating sets of modules

Published on 10 May 2026 - 17:19

score 1.1k · Answer 15 · 2026-05-10 13:23:24

1.1k

Views

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

Published on 10 May 2026 - 13:23

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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