List questions from dimension-theory-algebra

Published on 24 Mar 2026 - 15:28

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Dimension image of morphism of projective varieties

Published on 01 Feb 2019 - 16:22

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Hartshorne II.3.22c following the hint

Published on 23 Feb 2026 - 6:24

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Definition of codimension of variety

Published on 28 Feb 2019 - 11:57

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Dimension of product of varieties

Published on 22 Mar 2026 - 22:27

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Dimension of the orthogonal algebra?

Published on 19 Jun 2019 - 15:24

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Typo in Introduction to Commutative Algebra by Atiyah-Macdonald?

Published on 02 Aug 2019 - 10:19

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$V(I)$ consists of a finite set of points if and only $k[x_1,\ldots,x_n]/I$ has Krull dimension zero

Published on 04 Aug 2019 - 18:04

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Help Understanding Proof about Dimension Theory

Published on 05 Aug 2019 - 14:39

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The multiplicity of the intersection of two curves is the dimension of a certain vector space.

Published on 05 Aug 2019 - 17:10

263

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If $a_1,...,a_r$ is an $M$-regular sequence of maximal length, $M/(a_1,...,a_r)M$ has finite length.

Published on 12 Aug 2019 - 5:35

565

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The associated graded ring of the localization $k[x_1,\dots,x_n]_{(x_1,\dots,x_n)}$

Published on 21 Aug 2019 - 8:46

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Show that if the height of a prime ideal is zero, then it is a prime ideal belonging to 0

Published on 21 Aug 2019 - 8:57

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Complements of a subspace

Published on 10 Sep 2019 - 20:48

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If $X$ infinite dimensional and $F\colon X\to\mathbb{F}^{n}$ linear, then $\ker(F)$ infinite dimensional subspace of $X$.

Published on 30 Sep 2019 - 20:53

List Question

Hartshorne II-3.22(b)

Dimension image of morphism of projective varieties

Hartshorne II.3.22c following the hint

Definition of codimension of variety

Dimension of product of varieties

Dimension of the orthogonal algebra?

Typo in Introduction to Commutative Algebra by Atiyah-Macdonald?

$V(I)$ consists of a finite set of points if and only $k[x_1,\ldots,x_n]/I$ has Krull dimension zero

Help Understanding Proof about Dimension Theory

The multiplicity of the intersection of two curves is the dimension of a certain vector space.

If $a_1,...,a_r$ is an $M$-regular sequence of maximal length, $M/(a_1,...,a_r)M$ has finite length.

The associated graded ring of the localization $k[x_1,\dots,x_n]_{(x_1,\dots,x_n)}$

Show that if the height of a prime ideal is zero, then it is a prime ideal belonging to 0

Complements of a subspace

If $X$ infinite dimensional and $F\colon X\to\mathbb{F}^{n}$ linear, then $\ker(F)$ infinite dimensional subspace of $X$.

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