List questions from commutative-algebra

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If R is a semilocal Dedekind domain, then R is a PID.

Published on 25 Mar 2026 - 11:16

105

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Some question in computing Groebner basis

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Is the localization of intersection of modules equal to the intersection of appropriate localizations?

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292

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Find a reduced Groebner basis

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170

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Dimension of the irreducible components of intersection of a projective variety with zero set of homogeneous polynomial.

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97

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Calculating homology objects in this chain complex

Published on 11 Apr 2026 - 19:29

120

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Flat nilpotent ideals

Published on 10 Apr 2026 - 19:46

190

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$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Published on 25 Mar 2026 - 9:24

128

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Showing that $R \otimes_{R[X]} R[Y] \cong R[Y]/(Y^2)$

Published on 01 Apr 2026 - 17:37

38

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0-dimensional quasi projective variety

Published on 26 Mar 2026 - 22:17

154

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If $R$ is generically Gorenstein, then $\operatorname{Ann}(\operatorname{Ann}(I))=I$ for every ideal $I$ with non-zero annihilator?

Published on 10 Apr 2026 - 8:56

510

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Finite algebra over a ring is a field

Published on 11 Apr 2026 - 16:21

293

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The group of units of $K_0$ and the Picard group of a finitely generated regular $\mathbb Z$-algebra

Published on 07 Apr 2026 - 4:04

345

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Notation in Atiyah-Macdonald, Chapter 3, Exercise 21.iv

Published on 11 Apr 2026 - 12:19

List Question

Why is the Dimension of a Stalk Well Defined?

If R is a semilocal Dedekind domain, then R is a PID.

Some question in computing Groebner basis

Is the localization of intersection of modules equal to the intersection of appropriate localizations?

Find a reduced Groebner basis

Dimension of the irreducible components of intersection of a projective variety with zero set of homogeneous polynomial.

Calculating homology objects in this chain complex

Flat nilpotent ideals

$\mathrm{Ext}^1(N,M)=0$ for all cyclic modules $N$ implies $M$ is injective.

Showing that $R \otimes_{R[X]} R[Y] \cong R[Y]/(Y^2)$

0-dimensional quasi projective variety

If $R$ is generically Gorenstein, then $\operatorname{Ann}(\operatorname{Ann}(I))=I$ for every ideal $I$ with non-zero annihilator?

Finite algebra over a ring is a field

The group of units of $K_0$ and the Picard group of a finitely generated regular $\mathbb Z$-algebra

Notation in Atiyah-Macdonald, Chapter 3, Exercise 21.iv

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