Question

if R is a commutative ring in which all the maximal ideals are finitely generated then R is Noetherian?

score 28 · Answer 1 · 2024-03-15 10:06:12

28

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if R is a commutative ring in which all the maximal ideals are finitely generated then R is Noetherian?

Published on 15 Mar 2024 - 10:06

score 15 · Answer 2 · 2026-03-04 17:50:55

15

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Criterion for spanning and linear independence of the Zariski cotangent space of $R_p$ that doesn't use localization or quotient.

Published on 04 Mar 2026 - 17:50

score 15 · Answer 3 · 2026-03-04 17:50:56

15

Views

Let $A$ be a commutative local noetherian ring and let $I$ be a proper ideal of $A$. Prove that $\bigcap_{n=1}^\infty I^n = 0$.

Published on 04 Mar 2026 - 17:50

score 138 · Answer 4 · 2024-03-24 19:28:08

138

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Finding if an ideal is the radical of another one...

Published on 24 Mar 2024 - 19:28

score 73 · Answer 5 · 2026-03-29 13:48:55

73

Views

Localization using a prime ideal

Published on 29 Mar 2026 - 13:48

score 26 · Answer 6 · 2026-03-26 16:06:25

26

Views

Flat base change preserves the non-degeneracy (Proposition 9.2 in Commutative Algebra, Matsumura)

Published on 26 Mar 2026 - 16:06

score 79 · Answer 7 · 2024-03-27 18:34:36

79

Views

Prove that an ideal has height 2

Published on 27 Mar 2024 - 18:34

score 169 · Answer 8 · 2026-03-25 10:52:51

169

Views

Relation between lattice theorem in groups and in rings

Published on 25 Mar 2026 - 10:52

score 313 · Answer 9 · 2015-01-09 07:24:12

313

Views

Infinite intersection of prime ideals

Published on 09 Jan 2015 - 7:24

score 2.5k · Answer 10 · 2015-01-13 10:08:53

2.5k

Views

$R$ local ring, $I$ maximal ideal then $x\notin I$ implies $x$ unit

Published on 13 Jan 2015 - 10:08

score 387 · Answer 11 · 2015-01-15 10:00:16

387

Views

Finding a maximal ideal in the set of continuous real-valued functions on $\mathbb{R}$

Published on 15 Jan 2015 - 10:00

score 1.2k · Answer 12 · 2015-01-15 21:04:56

1.2k

Views

Prime ideals of infinite depth in Noetherian rings

Published on 15 Jan 2015 - 21:04

score 403 · Answer 13 · 2026-03-27 00:55:09

403

Views

Polynomial ring, prime ideal, factor ring

Published on 27 Mar 2026 - 0:55

score 205 · Answer 14 · 2015-01-18 07:00:49

205

Views

Maximal ideals of $R[x_1,\ldots,x_n]$ that is $R$ is a commutative rings with identity

Published on 18 Jan 2015 - 7:00

score 302 · Answer 15 · 2015-01-18 10:29:03

302

Views

Question about split monomorphisms of free modules over local rings

Published on 18 Jan 2015 - 10:29

List Question

if R is a commutative ring in which all the maximal ideals are finitely generated then R is Noetherian?

Criterion for spanning and linear independence of the Zariski cotangent space of $R_p$ that doesn't use localization or quotient.

Let $A$ be a commutative local noetherian ring and let $I$ be a proper ideal of $A$. Prove that $\bigcap_{n=1}^\infty I^n = 0$.

Finding if an ideal is the radical of another one...

Localization using a prime ideal

Flat base change preserves the non-degeneracy (Proposition 9.2 in Commutative Algebra, Matsumura)

Prove that an ideal has height 2

Relation between lattice theorem in groups and in rings

Infinite intersection of prime ideals

$R$ local ring, $I$ maximal ideal then $x\notin I$ implies $x$ unit

Finding a maximal ideal in the set of continuous real-valued functions on $\mathbb{R}$

Prime ideals of infinite depth in Noetherian rings

Polynomial ring, prime ideal, factor ring

Maximal ideals of $R[x_1,\ldots,x_n]$ that is $R$ is a commutative rings with identity

Question about split monomorphisms of free modules over local rings

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