List questions from noetherian

Published on 29 May 2022 - 19:20

454

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Two equivalent conditions on Serre's normality criterion

Published on 31 May 2022 - 11:47

222

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Proof explanation) Finite injective dimension of the residue field of a Noetherian local ring implies regularity

Published on 26 Mar 2026 - 1:18

178

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Dimension of the quotient ring of a Noetherian local ring by a principal ideal

Published on 26 Mar 2026 - 1:25

106

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Is the dual of a Noetherian module Noetherian?

Published on 11 Jun 2022 - 22:05

211

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Atiyah Macdonald Exercise 7.4

Published on 14 Jun 2022 - 15:44

108

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How do I show that $R=\Bbb{Z}_{(2)}\left[\sqrt{-3}\right]$ is a noetherian ring?

Published on 16 Jun 2022 - 13:49

68

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Is there an example where the Artin Rees lemma fails if we do not assume that $R$ is an integral domain?

Published on 22 Jun 2022 - 7:23

132

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Completion of the stalk of a flat scheme over a complete local Noetherian ring

Published on 25 Mar 2026 - 13:58

50

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Dimension of quotients of powers of maximal ideal

Published on 25 Mar 2026 - 23:39

175

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Hilbert's basis theorem?

Published on 29 Jun 2022 - 17:05

63

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Every non-zero-divisor in a Noetherian local ring is $\mathfrak{m}$-primary

Published on 29 Mar 2026 - 16:38

232

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$k[x]$ and its subfield as a finitely generated $k[t]$ Module

Published on 14 Jul 2022 - 22:47

54

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Noetherian ring with extra condition is a PID

Published on 08 Aug 2022 - 5:28

131

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Noetherian and Hausdorff space

Published on 25 Aug 2022 - 16:38

List Question

Let $R \subseteq S \subseteq R[X]$. Does $R$ noetherian imply $S$ is also Noetherian?

Two equivalent conditions on Serre's normality criterion

Proof explanation) Finite injective dimension of the residue field of a Noetherian local ring implies regularity

Dimension of the quotient ring of a Noetherian local ring by a principal ideal

Is the dual of a Noetherian module Noetherian?

Atiyah Macdonald Exercise 7.4

How do I show that $R=\Bbb{Z}_{(2)}\left[\sqrt{-3}\right]$ is a noetherian ring?

Is there an example where the Artin Rees lemma fails if we do not assume that $R$ is an integral domain?

Completion of the stalk of a flat scheme over a complete local Noetherian ring

Dimension of quotients of powers of maximal ideal

Hilbert's basis theorem?

Every non-zero-divisor in a Noetherian local ring is $\mathfrak{m}$-primary

$k[x]$ and its subfield as a finitely generated $k[t]$ Module

Noetherian ring with extra condition is a PID

Noetherian and Hausdorff space

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