List questions from krull-dimension

Published on 26 Mar 2026 - 2:55

130

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Show that the dimention of the intersection of projective linear sub-spaces of dimentions $d_1$ and $d_2$ of $\mathbb{P}^n$ is bigger than $d_1+d_2-n$

Published on 28 Mar 2026 - 21:06

231

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Regular local rings of Krull dimension $1$ are integral domains

Published on 29 Mar 2026 - 13:27

160

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Krull dimension of complement of an open subset containing all generic points

Published on 22 Dec 2021 - 0:54

139

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Krull dimension of $A[X,\sqrt{aX}]$, where $A$ is a PID.

Published on 10 Jan 2022 - 15:54

151

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Clarify on Krull dimension and integrality

Published on 18 Jan 2022 - 17:53

130

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All maximal chains have the same length in $k[x_1,\dots,x_n]$

Published on 18 Jan 2022 - 22:02

104

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Confusion on wording of an exercise about Krull dimension.

Published on 22 Jan 2022 - 0:32

313

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Transcendence degree and Krull dimension

Published on 22 Jan 2022 - 14:26

326

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Bound for the Krull dimension of a polynomial ring

Published on 28 Jan 2022 - 10:37

296

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Let $K[X,Y]$ be the polynomial ring in two variables over the field $K$. Show $\operatorname{dim}(K[X,Y]/(f))=1$ for any polynomial $f\in K[X,Y]$

Published on 28 Jan 2022 - 17:08

100

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$R/(a_1,\dots,a_r)$ is regular of dimension $d-r$ if and only if $\bar a_1,\dots,\bar a_r\in m/m^2$ are linearly independent

Published on 30 Jan 2022 - 10:25

146

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Equality of length of modules

Published on 02 Feb 2022 - 6:36

244

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Dimension of Blowup algebra

Published on 14 Feb 2022 - 7:14

54

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The (in?)validity of an argument showing that a certain ring is a Krull domain

Published on 29 Mar 2026 - 4:02

List Question

When $R/\operatorname{Ann}_R(M)$ is a Cohen-Macaulay ring?

Show that the dimention of the intersection of projective linear sub-spaces of dimentions $d_1$ and $d_2$ of $\mathbb{P}^n$ is bigger than $d_1+d_2-n$

Regular local rings of Krull dimension $1$ are integral domains

Krull dimension of complement of an open subset containing all generic points

Krull dimension of $A[X,\sqrt{aX}]$, where $A$ is a PID.

Clarify on Krull dimension and integrality

All maximal chains have the same length in $k[x_1,\dots,x_n]$

Confusion on wording of an exercise about Krull dimension.

Transcendence degree and Krull dimension

Bound for the Krull dimension of a polynomial ring

Let $K[X,Y]$ be the polynomial ring in two variables over the field $K$. Show $\operatorname{dim}(K[X,Y]/(f))=1$ for any polynomial $f\in K[X,Y]$

$R/(a_1,\dots,a_r)$ is regular of dimension $d-r$ if and only if $\bar a_1,\dots,\bar a_r\in m/m^2$ are linearly independent

Equality of length of modules

Dimension of Blowup algebra

The (in?)validity of an argument showing that a certain ring is a Krull domain

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