Question

Showing that the subalgebra $S$ of polynomials without linear terms of $k[x,y]$ is not finitely generated.

score 39 · Answer 1 · 2020-10-26 21:53:23

39

Views

Showing that the subalgebra $S$ of polynomials without linear terms of $k[x,y]$ is not finitely generated.

Published on 26 Oct 2020 - 21:53

score 540 · Answer 2 · 2026-03-28 17:05:36

540

Views

How can a polynomial ring be finitely generated?

Published on 28 Mar 2026 - 17:05

score 52 · Answer 3 · 2026-03-27 05:39:02

52

Views

Free group on a set B. If the free group is finitely generated, then B is finite.

Published on 27 Mar 2026 - 5:39

score 222 · Answer 4 · 2020-11-07 15:06:08

222

Views

Why would a natural isomorphism $A \cong TA \oplus (A / TA)$ imply that $A \twoheadrightarrow A/TA \rightarrowtail TA \oplus (A / TA)$ is natural?

Published on 07 Nov 2020 - 15:06

score 113 · Answer 5 · 2026-03-25 22:06:35

113

Views

The rank of torsion free nilpotent group

Published on 25 Mar 2026 - 22:06

score 83 · Answer 6 · 2020-11-12 02:42:05

83

Views

A group as the union of finitely generated subgroups

Published on 12 Nov 2020 - 2:42

score 112 · Answer 7 · 2026-03-27 07:11:38

112

Views

Are solvable groups Howson?

Published on 27 Mar 2026 - 7:11

score 57 · Answer 8 · 2020-11-14 14:35:05

57

Views

If the orders of all elements of a group are uniformly bounded by some finite number, is every finitely generated subgroup finite?

Published on 14 Nov 2020 - 14:35

score 86 · Answer 9 · 2020-11-15 07:22:39

86

Views

Prove that $G$ is a finitely generated group under multiplication.

Published on 15 Nov 2020 - 7:22

score 104 · Answer 10 · 2020-11-17 19:20:02

104

Views

$J:=M+\langle a\rangle $ how can I show that this ideal is generated by $\langle m_1,..., m_n,a \rangle$ and that $M \subsetneq J$?

Published on 17 Nov 2020 - 19:20

score 170 · Answer 11 · 2020-11-18 02:04:55

170

Views

Prove that if every family $\mathcal{C}$ of ideals in $R$ has a maximal element then every ideal is finitely generated.

Published on 18 Nov 2020 - 2:04

score 671 · Answer 12 · 2026-03-29 07:40:28

671

Views

Checking the proof that if every ideal of $R$ is finitely generated then $R$ is Noetherian.

Published on 29 Mar 2026 - 7:40

score 64 · Answer 13 · 2020-11-21 19:33:08

64

Views

Unified theory of finitely generated groups and Lie groups

Published on 21 Nov 2020 - 19:33

score 30 · Answer 14 · 2020-11-24 14:05:31

30

Views

If the union of finitely many conjugacy classes is syndetic, are there finitely many conjugacy classes?

Published on 24 Nov 2020 - 14:05

score 132 · Answer 15 · 2020-11-27 23:40:36

132

Views

Groups generated by the subset of integer powers of group elements.

Published on 27 Nov 2020 - 23:40

List Question

Showing that the subalgebra $S$ of polynomials without linear terms of $k[x,y]$ is not finitely generated.

How can a polynomial ring be finitely generated?

Free group on a set B. If the free group is finitely generated, then B is finite.

Why would a natural isomorphism $A \cong TA \oplus (A / TA)$ imply that $A \twoheadrightarrow A/TA \rightarrowtail TA \oplus (A / TA)$ is natural?

The rank of torsion free nilpotent group

A group as the union of finitely generated subgroups

Are solvable groups Howson?

If the orders of all elements of a group are uniformly bounded by some finite number, is every finitely generated subgroup finite?

Prove that $G$ is a finitely generated group under multiplication.

$J:=M+\langle a\rangle $ how can I show that this ideal is generated by $\langle m_1,..., m_n,a \rangle$ and that $M \subsetneq J$?

Prove that if every family $\mathcal{C}$ of ideals in $R$ has a maximal element then every ideal is finitely generated.

Checking the proof that if every ideal of $R$ is finitely generated then $R$ is Noetherian.

Unified theory of finitely generated groups and Lie groups

If the union of finitely many conjugacy classes is syndetic, are there finitely many conjugacy classes?

Groups generated by the subset of integer powers of group elements.

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