Question

Let $R$ be a ring and $I$ be a finitely generated nilpotent ideal. If $R/I$ is noetherian (resp. Artinian) then $R$ is so.

score 376 · Answer 1 · 2016-04-04 07:14:02

376

Views

Let $R$ be a ring and $I$ be a finitely generated nilpotent ideal. If $R/I$ is noetherian (resp. Artinian) then $R$ is so.

Published on 04 Apr 2016 - 7:14

score 492 · Answer 2 · 2016-04-09 08:18:52

492

Views

Proof of commutative Artinian ring is Noetherian

Published on 09 Apr 2016 - 8:18

score 1.7k · Answer 3 · 2016-04-09 16:38:27

1.7k

Views

Noetherian local ring is Artinian iff maximal ideal is nilpotent

Published on 09 Apr 2016 - 16:38

score 2.8k · Answer 4 · 2016-04-14 00:23:43

2.8k

Views

A Bézout UFD is a PID.

Published on 14 Apr 2016 - 0:23

score 1.3k · Answer 5 · 2016-04-18 13:07:56

1.3k

Views

Noether's normalization lemma in practice (example)

Published on 18 Apr 2016 - 13:07

score 142 · Answer 6 · 2016-04-18 21:03:16

142

Views

If $A$ is a commutative, unitary ring and $I$ an ideal of $A$ such that $I$ and $A/I$ are Noetherian rings, then $A$ is Noetherian?

Published on 18 Apr 2016 - 21:03

score 235 · Answer 7 · 2026-03-25 17:13:07

235

Views

About a short proof of Krull principal ideal theorem

Published on 25 Mar 2026 - 17:13

score 75 · Answer 8 · 2026-03-24 02:22:19

75

Views

Question about proof of Krull principal ideal theorem

Published on 24 Mar 2026 - 2:22

score 289 · Answer 9 · 2026-03-25 15:44:02

289

Views

Artinian - Noetherian rings and modules suggest study guide

Published on 25 Mar 2026 - 15:44

score 455 · Answer 10 · 2016-04-28 14:58:57

455

Views

$R$ be a commutative ring with unity such that every surjective ring homomorphism $f:R\to R$ is injective, then is $R$ Noetherian?

Published on 28 Apr 2016 - 14:58

score 28 · Answer 11 · 2016-05-01 07:37:29

28

Views

The product $JR$ of a proper ideal $J$ and the nontrivial ideal $R$

Published on 01 May 2016 - 7:37

score 760 · Answer 12 · 2016-05-03 15:28:24

760

Views

System of parameters in Noetherian local rings

Published on 03 May 2016 - 15:28

score 966 · Answer 13 · 2016-05-14 08:20:51

966

Views

If $R/I$ and $R/J$ are Noetherian (resp. Artinian), then so is $R/(I \cap J)$

Published on 14 May 2016 - 8:20

score 541 · Answer 14 · 2016-05-15 08:28:25

541

Views

If $I$ is finitely generated nilpotent and $R/I^{n-1}$ is noetherian then $R$ is noetherian

Published on 15 May 2016 - 8:28

score 101 · Answer 15 · 2016-05-17 18:33:23

If every ideal I in R is contained in a finite series of ascending ideals, prove that only finitely many ideals of any kind contain I.

List Question

Let $R$ be a ring and $I$ be a finitely generated nilpotent ideal. If $R/I$ is noetherian (resp. Artinian) then $R$ is so.

Proof of commutative Artinian ring is Noetherian

Noetherian local ring is Artinian iff maximal ideal is nilpotent

A Bézout UFD is a PID.

Noether's normalization lemma in practice (example)

If $A$ is a commutative, unitary ring and $I$ an ideal of $A$ such that $I$ and $A/I$ are Noetherian rings, then $A$ is Noetherian?

About a short proof of Krull principal ideal theorem

Question about proof of Krull principal ideal theorem

Artinian - Noetherian rings and modules suggest study guide

$R$ be a commutative ring with unity such that every surjective ring homomorphism $f:R\to R$ is injective, then is $R$ Noetherian?

The product $JR$ of a proper ideal $J$ and the nontrivial ideal $R$

System of parameters in Noetherian local rings

If $R/I$ and $R/J$ are Noetherian (resp. Artinian), then so is $R/(I \cap J)$

If $I$ is finitely generated nilpotent and $R/I^{n-1}$ is noetherian then $R$ is noetherian

If every ideal I in R is contained in a finite series of ascending ideals, prove that only finitely many ideals of any kind contain I.

Trending Questions

Popular # Hahtags

Popular Questions