Question

Let $M$ be a noetherian $R$-module and $I=\mathrm{Ann}_R(M)$. Then $R/I$ is a noetherian ring for all ring $R$?

score 241 · Answer 1 · 2020-12-20 04:21:05

241

Views

Let $M$ be a noetherian $R$-module and $I=\mathrm{Ann}_R(M)$. Then $R/I$ is a noetherian ring for all ring $R$?

Published on 20 Dec 2020 - 4:21

score 304 · Answer 2 · 2020-12-20 11:58:37

304

Views

Proof of Eakin-Nagata theorem, Matsumura $thm2.6$

Published on 20 Dec 2020 - 11:58

score 70 · Answer 3 · 2020-12-21 13:41:32

70

Views

Must the endomorphism ring of a finitely generated module be Noetherian?

Published on 21 Dec 2020 - 13:41

score 169 · Answer 4 · 2020-12-21 17:21:13

169

Views

Is $\mathbb{Z}[2x, 2x^2 , 2x^3 , \cdots ]$ noetherian

Published on 21 Dec 2020 - 17:21

score 121 · Answer 5 · 2026-03-25 17:42:28

121

Views

Can the union of an ascending sequence of ideals of $R$ be $R$?

Published on 25 Mar 2026 - 17:42

score 222 · Answer 6 · 2020-12-27 20:03:58

222

Views

If $A$ is a commutative Noetherian ring, then $D=\lbrace\mathfrak{p}\in \operatorname{Spec}(A): |A/\mathfrak{p}|\leq k\rbrace$ is a finite set.

Published on 27 Dec 2020 - 20:03

score 204 · Answer 7 · 2020-12-29 01:50:20

204

Views

Is Kernel of a map from free module to finitely generated graded module graded?

Published on 29 Dec 2020 - 1:50

score 289 · Answer 8 · 2020-12-30 09:26:56

289

Views

Ring is Noetherian if it admits a faithful finitely generated module with ACC on submodules generated by ideals

Published on 30 Dec 2020 - 9:26

score 126 · Answer 9 · 2026-03-26 17:35:02

126

Views

Finite Presentations on Graded $A$-modules over Noetherian rings.

Published on 26 Mar 2026 - 17:35

score 414 · Answer 10 · 2026-03-27 16:37:20

414

Views

Is a Noetherian graded ring also a finitely generated $R_0$-module?

Published on 27 Mar 2026 - 16:37

score 227 · Answer 11 · 2021-01-02 13:32:45

227

Views

Non-Noetherian subring of $\mathbb{C}[X,Y]$

Published on 02 Jan 2021 - 13:32

score 100 · Answer 12 · 2021-01-03 13:21:20

100

Views

$\mathbb{C\otimes_QC} $ is not Noether ring, but $\operatorname{Spec}(\mathbb{C\otimes_QC})$ is Noether as topological space

Published on 03 Jan 2021 - 13:21

score 733 · Answer 13 · 2021-01-09 09:13:18

733

Views

If $M/N_1, M/N_2$ are Noetherian then $M/(N_1∩N_2)$ is Noetherian.

Published on 09 Jan 2021 - 9:13

score 401 · Answer 14 · 2026-03-25 21:44:59

401

Views

An artinian ring is Noetherian

Published on 25 Mar 2026 - 21:44

score 123 · Answer 15 · 2021-01-14 09:44:25

123

Views

Maximal ideal in noetherian local ring

Published on 14 Jan 2021 - 9:44

List Question

Let $M$ be a noetherian $R$-module and $I=\mathrm{Ann}_R(M)$. Then $R/I$ is a noetherian ring for all ring $R$?

Proof of Eakin-Nagata theorem, Matsumura $thm2.6$

Must the endomorphism ring of a finitely generated module be Noetherian?

Is $\mathbb{Z}[2x, 2x^2 , 2x^3 , \cdots ]$ noetherian

Can the union of an ascending sequence of ideals of $R$ be $R$?

If $A$ is a commutative Noetherian ring, then $D=\lbrace\mathfrak{p}\in \operatorname{Spec}(A): |A/\mathfrak{p}|\leq k\rbrace$ is a finite set.

Is Kernel of a map from free module to finitely generated graded module graded?

Ring is Noetherian if it admits a faithful finitely generated module with ACC on submodules generated by ideals

Finite Presentations on Graded $A$-modules over Noetherian rings.

Is a Noetherian graded ring also a finitely generated $R_0$-module?

Non-Noetherian subring of $\mathbb{C}[X,Y]$

$\mathbb{C\otimes_QC} $ is not Noether ring, but $\operatorname{Spec}(\mathbb{C\otimes_QC})$ is Noether as topological space

If $M/N_1, M/N_2$ are Noetherian then $M/(N_1∩N_2)$ is Noetherian.

An artinian ring is Noetherian

Maximal ideal in noetherian local ring

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