List questions from commutative-algebra

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Isomorphism of ring localized twice - Atiyah Macdonald Exercise 3.3

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Matsumura Example 2 (16.E)

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Sum and product of comaximal ideals

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Commutative Algebra and Game Theory

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$\overline{\mathbb{Z}}$ is not a Dedekind domain.

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UFD and relatively prime elements

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Show that the ring of continuous functions $f:\mathbb R\to\mathbb R$ is not Noetherian

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Normalization of a variety

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If $\mathcal{I}(-)$ is the ideal map on subsets of affine space, why does $A\subseteq\overline{B}\iff\mathcal{I}(B)\subseteq\mathcal{I}(A)$?

Published on 13 Apr 2026 - 2:00

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Hartshorne II Prop 6.8

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Factorization in Dedekind domains

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If $0\to M'\to M\to M''\to 0$ is exact, why does $\operatorname{Ass}(M)\subseteq \operatorname{Ass}(M')\cup \operatorname{Ass}(M'')$.

Published on 16 Apr 2026 - 22:16

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A set $S\subseteq\mathbb{A}^n$ is quasi-affine iff $S=Z\setminus V$ for closed $Z$ and $U$?

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Krull dimension of a finitely generated integral domain over $k$ is equal to the transcendence degree.

Published on 12 Apr 2026 - 16:09

List Question

The krull dimension of $\Bbb{Z}$ and artinian rings

Isomorphism of ring localized twice - Atiyah Macdonald Exercise 3.3

Matsumura Example 2 (16.E)

Sum and product of comaximal ideals

Commutative Algebra and Game Theory

$\overline{\mathbb{Z}}$ is not a Dedekind domain.

UFD and relatively prime elements

Show that the ring of continuous functions $f:\mathbb R\to\mathbb R$ is not Noetherian

Normalization of a variety

If $\mathcal{I}(-)$ is the ideal map on subsets of affine space, why does $A\subseteq\overline{B}\iff\mathcal{I}(B)\subseteq\mathcal{I}(A)$?

Hartshorne II Prop 6.8

Factorization in Dedekind domains

If $0\to M'\to M\to M''\to 0$ is exact, why does $\operatorname{Ass}(M)\subseteq \operatorname{Ass}(M')\cup \operatorname{Ass}(M'')$.

A set $S\subseteq\mathbb{A}^n$ is quasi-affine iff $S=Z\setminus V$ for closed $Z$ and $U$?

Krull dimension of a finitely generated integral domain over $k$ is equal to the transcendence degree.

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