Question

Finitely generated $k$-algebras beginner examples.

score 531 · Answer 1 · 2026-03-25 02:57:53

531

Views

Finitely generated $k$-algebras beginner examples.

Published on 25 Mar 2026 - 2:57

score 91 · Answer 2 · 2019-01-28 16:36:54

91

Views

$\mathbb{Z}[1/3]$ is not finitely generated as a $\mathbb{Z}$-module.

Published on 28 Jan 2019 - 16:36

score 73 · Answer 3 · 2019-01-30 07:58:42

73

Views

How to show that $\#(\mathbb Z^n/N) = \det(A)$ where $N$ is the subgroup of $\mathbb Z^n$ generated by columns of a square matrix $A$

Published on 30 Jan 2019 - 7:58

score 140 · Answer 4 · 2019-01-30 19:14:22

140

Views

Why is $Z^n/AZ^n \cong Z/d_1Z\oplus Z/d_2Z..$ where $d_i$ are the entries of normal form of A?

Published on 30 Jan 2019 - 19:14

score 69 · Answer 5 · 2019-01-30 19:49:14

69

Views

Dimension of span of a finitely generated subgroup

Published on 30 Jan 2019 - 19:49

score 59 · Answer 6 · 2026-03-25 11:02:20

59

Views

Could $\langle \Gamma | R \rangle \cong \langle \Gamma | S\rangle$ if $\langle R\rangle \subsetneq \langle S\rangle$?

Published on 25 Mar 2026 - 11:02

score 40 · Answer 7 · 2019-02-09 19:55:24

40

Views

Quick proof that $SL_2(\mathbb Z/n\mathbb Z)\cong \oplus_{p\mid n}SL_2(\mathbb Z/p^{e_p}\mathbb Z)$

Published on 09 Feb 2019 - 19:55

score 231 · Answer 8 · 2026-03-25 09:28:55

231

Views

Can I conclude that my group is finitely generated, if it is a homomorphic image of a free-group on finitely many generators?

Published on 25 Mar 2026 - 9:28

score 515 · Answer 9 · 2019-02-19 02:00:20

515

Views

Set of all R-homomorphism is finitely generated

Published on 19 Feb 2019 - 2:00

score 50 · Answer 10 · 2019-02-19 11:31:09

50

Views

Does a finitely generated group $G$, ever act on $G/N$ freely?

Published on 19 Feb 2019 - 11:31

score 62 · Answer 11 · 2019-02-23 14:26:32

62

Views

Isomorphism between finitely generated projective modules over algebra of functions

Published on 23 Feb 2019 - 14:26

score 81 · Answer 12 · 2026-03-25 04:40:35

81

Views

Finite generation of cones in $\mathbf{Z}^n$

Published on 25 Mar 2026 - 4:40

score 157 · Answer 13 · 2019-03-05 12:33:37

157

Views

Proving $G \ast_A$ finitely presented $\Leftrightarrow$ $A$ finitely generated

Published on 05 Mar 2019 - 12:33

score 308 · Answer 14 · 2026-03-25 06:09:45

308

Views

Why all nilpotent and finitely generated groups are Max?

Published on 25 Mar 2026 - 6:09

score 119 · Answer 15 · 2026-03-25 06:39:29

119

Views

Need help understanding a step in a proof about modules over PIDs

Published on 25 Mar 2026 - 6:39

List Question

Finitely generated $k$-algebras beginner examples.

$\mathbb{Z}[1/3]$ is not finitely generated as a $\mathbb{Z}$-module.

How to show that $\#(\mathbb Z^n/N) = \det(A)$ where $N$ is the subgroup of $\mathbb Z^n$ generated by columns of a square matrix $A$

Why is $Z^n/AZ^n \cong Z/d_1Z\oplus Z/d_2Z..$ where $d_i$ are the entries of normal form of A?

Dimension of span of a finitely generated subgroup

Could $\langle \Gamma | R \rangle \cong \langle \Gamma | S\rangle$ if $\langle R\rangle \subsetneq \langle S\rangle$?

Quick proof that $SL_2(\mathbb Z/n\mathbb Z)\cong \oplus_{p\mid n}SL_2(\mathbb Z/p^{e_p}\mathbb Z)$

Can I conclude that my group is finitely generated, if it is a homomorphic image of a free-group on finitely many generators?

Set of all R-homomorphism is finitely generated

Does a finitely generated group $G$, ever act on $G/N$ freely?

Isomorphism between finitely generated projective modules over algebra of functions

Finite generation of cones in $\mathbf{Z}^n$

Proving $G \ast_A$ finitely presented $\Leftrightarrow$ $A$ finitely generated

Why all nilpotent and finitely generated groups are Max?

Need help understanding a step in a proof about modules over PIDs

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