List questions from noetherian

Published on 08 May 2021 - 11:50

457

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Why do we need Noetherianness to conclude that a connected scheme is integral iff its local rings are?

Published on 09 May 2021 - 15:36

245

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Suppose that $R$ is not a noetherian ring. Then can we have an ideal in $R[x_1,...,x_n]$ which is not finitely generated?

Published on 10 May 2021 - 7:13

387

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Is the ring $\mathbb{C}[x,y]/(x^2,y^3)$ Artinian? If not, what is its Krull dimension?

Published on 25 Mar 2026 - 23:22

823

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If $R$ is a Noetherian ring and $I$ a proper ideal, then the $R$-module $R/I$ has finite length iff the associated primes of $I$ are maximal

Published on 15 May 2021 - 20:48

246

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$S^{-1}M$ is a Noetherian $S^{-1}R$ module

Published on 17 May 2021 - 10:32

81

Views

Direct sum of completions is faithfully flat

Published on 19 May 2021 - 11:29

89

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Prove that if $\mathrm{gr}(A)$ is Noetherian without zero-divisors, then so is $A$.

Published on 27 Mar 2026 - 0:58

32

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Exact functors in local cohomology

Published on 28 Mar 2026 - 10:40

170

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Proposition 9.2 (iv)=>(v) Atiyah: why principal?

Published on 24 May 2021 - 12:44

55

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A question about a Noetherian ring starting from a subring

Published on 25 Mar 2026 - 23:19

399

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Artinian, but not Noetherian module: a wonderful example.

Published on 25 Mar 2026 - 23:19

240

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$\mathbb{Z}+x \cdot \mathbb{Q}[x]$ is not noetherian

Published on 13 Jun 2021 - 8:43

220

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Example of non-reduced Noetherian dimension 1 Cohen-Macaulay ring.

Published on 26 Mar 2026 - 4:32

203

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Conditions such that the completion of a domain is still a domain

Published on 17 Jun 2021 - 19:12

List Question

non noetherian rings

Why do we need Noetherianness to conclude that a connected scheme is integral iff its local rings are?

Suppose that $R$ is not a noetherian ring. Then can we have an ideal in $R[x_1,...,x_n]$ which is not finitely generated?

Is the ring $\mathbb{C}[x,y]/(x^2,y^3)$ Artinian? If not, what is its Krull dimension?

If $R$ is a Noetherian ring and $I$ a proper ideal, then the $R$-module $R/I$ has finite length iff the associated primes of $I$ are maximal

$S^{-1}M$ is a Noetherian $S^{-1}R$ module

Direct sum of completions is faithfully flat

Prove that if $\mathrm{gr}(A)$ is Noetherian without zero-divisors, then so is $A$.

Exact functors in local cohomology

Proposition 9.2 (iv)=>(v) Atiyah: why principal?

A question about a Noetherian ring starting from a subring

Artinian, but not Noetherian module: a wonderful example.

$\mathbb{Z}+x \cdot \mathbb{Q}[x]$ is not noetherian

Example of non-reduced Noetherian dimension 1 Cohen-Macaulay ring.

Conditions such that the completion of a domain is still a domain

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