Question

Show that $R$ is a Noetherian Ring

score 396 · Answer 1 · 2026-03-28 10:17:19

396

Views

Show that $R$ is a Noetherian Ring

Published on 28 Mar 2026 - 10:17

score 294 · Answer 2 · 2026-03-25 20:15:46

294

Views

Endomorphism of a local $k$-algebra inducing an automorphism modulo $m^2$ is an automorphism

Published on 25 Mar 2026 - 20:15

score 480 · Answer 3 · 2014-02-24 15:11:04

480

Views

If an $A$-module $M$ is locally finitely presented (resp. related) then $M$ is finitely presented (resp. related)

Published on 24 Feb 2014 - 15:11

score 779 · Answer 4 · 2026-03-25 19:03:26

779

Views

"M is reflexive" implies "M is maximal Cohen-Macaulay". Is the converse true?

Published on 25 Mar 2026 - 19:03

score 2.5k · Answer 5 · 2014-03-09 15:35:36

2.5k

Views

Localization of a module is zero implies the multiplicatively closed subset contains a single element annihilating the module

Published on 09 Mar 2014 - 15:35

score 420 · Answer 6 · 2017-04-12 16:03:19

420

Views

Is the quotient $\Bbb{Z}[X]/(f)$ finitely generated as an abelian group only if $f$ is monic?

Published on 12 Apr 2017 - 16:03

score 107 · Answer 7 · 2017-04-15 02:08:16

107

Views

Identities in groups having long proofs

Published on 15 Apr 2017 - 2:08

score 110 · Answer 8 · 2026-02-23 04:56:24

110

Views

Showing $\mathscr{P}_n=\langle\zeta, \tau, \pi, \xi\rangle$.

Published on 23 Feb 2026 - 4:56

score 113 · Answer 9 · 2017-04-28 07:27:30

113

Views

Is $Z$ generated by $\pm 1$ as a ring

Published on 28 Apr 2017 - 7:27

score 69 · Answer 10 · 2017-04-28 15:24:41

69

Views

If $R$ is a commutative ring with ideal $I$, $a \in R$; implications of $I + Ra$ being finitely generated

Published on 28 Apr 2017 - 15:24

score 119 · Answer 11 · 2026-03-28 15:46:01

119

Views

If G has solvable word problem, then word metric $d_{S}(e,w)$ is computable.

Published on 28 Mar 2026 - 15:46

score 97 · Answer 12 · 2017-05-24 16:54:25

97

Views

Looking for a generalization of Wedderburn's Little theorem with weaker hypothesis

Published on 24 May 2017 - 16:54

score 51 · Answer 13 · 2026-03-27 17:06:06

51

Views

In nilpotent groups, does $\forall a\in G [a,[a,x]]=1$ imply $\forall a\in G [a,x]\in Z(G)$

Published on 27 Mar 2026 - 17:06

score 545 · Answer 14 · 2026-03-29 06:28:47

545

Views

Finitely generated torsion-free module is free

Published on 29 Mar 2026 - 6:28

score 49 · Answer 15 · 2017-06-16 15:21:20

49

Views

Show that $\mathbb{Z}'_\mathbb{C}$ is not a finitely generated $\mathbb{Z}$-module.

Published on 16 Jun 2017 - 15:21

List Question

Show that $R$ is a Noetherian Ring

Endomorphism of a local $k$-algebra inducing an automorphism modulo $m^2$ is an automorphism

If an $A$-module $M$ is locally finitely presented (resp. related) then $M$ is finitely presented (resp. related)

"M is reflexive" implies "M is maximal Cohen-Macaulay". Is the converse true?

Localization of a module is zero implies the multiplicatively closed subset contains a single element annihilating the module

Is the quotient $\Bbb{Z}[X]/(f)$ finitely generated as an abelian group only if $f$ is monic?

Identities in groups having long proofs

Showing $\mathscr{P}_n=\langle\zeta, \tau, \pi, \xi\rangle$.

Is $Z$ generated by $\pm 1$ as a ring

If $R$ is a commutative ring with ideal $I$, $a \in R$; implications of $I + Ra$ being finitely generated

If G has solvable word problem, then word metric $d_{S}(e,w)$ is computable.

Looking for a generalization of Wedderburn's Little theorem with weaker hypothesis

In nilpotent groups, does $\forall a\in G [a,[a,x]]=1$ imply $\forall a\in G [a,x]\in Z(G)$

Finitely generated torsion-free module is free

Show that $\mathbb{Z}'_\mathbb{C}$ is not a finitely generated $\mathbb{Z}$-module.

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