List questions from commutative-algebra

Published on 11 Jul 2018 - 15:23

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basic question flatness and non-zero divisors: $B/fB$ flat implies $f$ is a non-zero divisor

Published on 11 Jul 2018 - 21:00

96

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Property for Kähler Differentials

Published on 25 Mar 2026 - 9:24

108

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For rings $R,S$ with $R \subseteq S$, $S \otimes_{R} R[x] \cong S[x]$ as $R$-modules

Published on 27 Mar 2026 - 23:37

293

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$\mathbb{Z}_{(p)}[\zeta]$ principal ideal domain

Published on 25 Mar 2026 - 14:38

184

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Relationship between cyclotomic polynomials

Published on 25 Mar 2026 - 20:39

198

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A Noetherian ring which is not a Noetherian $R$-module

Published on 25 Mar 2026 - 2:59

292

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When do we know a quotient of the polynomial ring over a local ring is torsion-free?

Published on 25 Mar 2026 - 17:21

348

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Can a non-PID noetherian integral domain have all PID localizations?

Published on 25 Mar 2026 - 3:01

114

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If $A\subset B$ is faithfully flat and $B$ is finitely presented, is $A$ finitely presented?

Published on 15 Jul 2018 - 16:04

224

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Primitive roots of unity and $I$-adically separated rings.

Published on 26 Mar 2026 - 3:11

441

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Action of torus on an affine toric variety

Published on 25 Mar 2026 - 3:04

102

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Ideal of an ideal being an ideal itself

Published on 16 Jul 2018 - 8:35

1k

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Is a local ring Artinian, if the maximal ideal is nilpotent?

Published on 25 Mar 2026 - 4:39

93

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Is the Noetherian condition of $R$ really necessary here?

Published on 27 Mar 2026 - 23:32

List Question

example of a hilbert series

basic question flatness and non-zero divisors: $B/fB$ flat implies $f$ is a non-zero divisor

Property for Kähler Differentials

For rings $R,S$ with $R \subseteq S$, $S \otimes_{R} R[x] \cong S[x]$ as $R$-modules

$\mathbb{Z}_{(p)}[\zeta]$ principal ideal domain

Relationship between cyclotomic polynomials

A Noetherian ring which is not a Noetherian $R$-module

When do we know a quotient of the polynomial ring over a local ring is torsion-free?

Can a non-PID noetherian integral domain have all PID localizations?

If $A\subset B$ is faithfully flat and $B$ is finitely presented, is $A$ finitely presented?

Primitive roots of unity and $I$-adically separated rings.

Action of torus on an affine toric variety

Ideal of an ideal being an ideal itself

Is a local ring Artinian, if the maximal ideal is nilpotent?

Is the Noetherian condition of $R$ really necessary here?

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