Question

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

score 589 · Answer 1 · 2026-04-10 23:14:18

589

Views

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

Published on 10 Apr 2026 - 23:14

score 55 · Answer 2 · 2026-04-14 23:06:36

55

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 14 Apr 2026 - 23:06

score 55 · Answer 3 · 2026-04-15 03:57:05

55

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 15 Apr 2026 - 3:57

score 1.1k · Answer 4 · 2026-04-11 14:44:37

1.1k

Views

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

Published on 11 Apr 2026 - 14:44

score 317 · Answer 5 · 2026-04-16 07:06:41

317

Views

How can I find a finite generating set for the ideal $I \subset \mathbb C[x,y]$ generated by the set $\{y -x,y - x^2, y-x^3,\dots\}$?

Published on 16 Apr 2026 - 7:06

score 229 · Answer 6 · 2026-04-15 06:36:20

229

Views

For a finitely generated $K$ algebra $A$ is $S^{-1}A$ also finitely generated $K$ algebra?

Published on 15 Apr 2026 - 6:36

score 172 · Answer 7 · 2026-04-11 15:33:00

172

Views

Is $\mathbb{Z}[x]/(2x^2)$ a finitely generated $\mathbb{Z}$ module?

Published on 11 Apr 2026 - 15:33

score 45 · Answer 8 · 2026-05-10 11:39:51

45

Views

Vector space dimension after nonlinearly mapping spanning vectors

Published on 10 May 2026 - 11:39

score 192 · Answer 9 · 2026-04-15 12:43:27

192

Views

"Dimension inequality" preserving linear map for vector spaces

Published on 15 Apr 2026 - 12:43

score 582 · Answer 10 · 2026-04-14 18:31:07

582

Views

$M$ is a cyclic module if and only if it has a single invariant factor

Published on 14 Apr 2026 - 18:31

score 364 · Answer 11 · 2026-04-10 16:37:28

364

Views

Cancellation for finitely generated abelian groups

Published on 10 Apr 2026 - 16:37

score 552 · Answer 12 · 2026-04-14 05:28:55

552

Views

If the $R$-module $M$ is finitely generated, but some generating set is not linearly independent, is $M$ not free?

Published on 14 Apr 2026 - 5:28

score 115 · Answer 13 · 2026-04-14 17:12:39

115

Views

Prime decomposition in a Dedekind domain

Published on 14 Apr 2026 - 17:12

score 143 · Answer 14 · 2026-04-11 21:02:25

143

Views

Noether normalization: what is a finite map?

Published on 11 Apr 2026 - 21:02

score 145 · Answer 15 · 2026-04-17 00:44:09

145

Views

Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$

Published on 17 Apr 2026 - 0:44

List Question

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

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 $M$

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

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

How can I find a finite generating set for the ideal $I \subset \mathbb C[x,y]$ generated by the set $\{y -x,y - x^2, y-x^3,\dots\}$?

For a finitely generated $K$ algebra $A$ is $S^{-1}A$ also finitely generated $K$ algebra?

Is $\mathbb{Z}[x]/(2x^2)$ a finitely generated $\mathbb{Z}$ module?

Vector space dimension after nonlinearly mapping spanning vectors

"Dimension inequality" preserving linear map for vector spaces

$M$ is a cyclic module if and only if it has a single invariant factor

Cancellation for finitely generated abelian groups

If the $R$-module $M$ is finitely generated, but some generating set is not linearly independent, is $M$ not free?

Prime decomposition in a Dedekind domain

Noether normalization: what is a finite map?

Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$

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