List questions from krull-dimension

Published on 24 Apr 2017 - 8:53

123

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Which is the Krull dimension of $\frac{\mathbb{K}[X_1,X_2]}{(X_1X_2)}$?

Published on 05 May 2017 - 10:34

136

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How can I show $\mathbb Z[\sqrt{-3}]$ is one dimensional?

Published on 08 May 2017 - 14:55

126

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Why $\dim(R/\mathrm{Jac}(R))=0$ for Dedekind domain $R$ with $\mathrm{Jac}(R)\neq 0$?

Published on 26 Mar 2026 - 21:26

697

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Krull dimension of the ring $K[t^{-1},t]$

Published on 25 Mar 2026 - 14:33

694

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When is $\dim R_f = \dim R$?

Published on 20 May 2017 - 13:29

399

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Example of a Noetherian local ring of dimension one which is not a discrete valuation ring.

Published on 28 Mar 2026 - 8:35

47

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$\mu_R(m)\geq \dim R$ where $\mu_R(m)=\operatorname{embdim}R$.

Published on 23 May 2017 - 11:56

42

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Find dimension and depth of $R=S_{P}/[(x,y)\cap (z,w)]S_{P}$

Published on 24 May 2017 - 16:19

37

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Koszul applied to dimension theory

Published on 06 Jun 2017 - 13:52

456

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Final step of exercise 11.7 from Atiyah-Macdonald ($\dim A[x]=\dim A+1$)

Published on 25 Mar 2026 - 16:08

149

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Dimension formula

Published on 14 Jun 2017 - 4:57

177

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Give an example of ring that has two maximal chains of prime ideals of different lengths.

Published on 15 Jun 2017 - 18:00

868

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Dimension of a product of projective varieties

Published on 20 Jun 2017 - 20:01

124

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Computing $\dim (\mathbb{Q} + x \mathbb{R}[x])$

Published on 28 Jun 2017 - 10:32

List Question

why zero dimensional reduced ring are Von Neumann Regular?

Which is the Krull dimension of $\frac{\mathbb{K}[X_1,X_2]}{(X_1X_2)}$?

How can I show $\mathbb Z[\sqrt{-3}]$ is one dimensional?

Why $\dim(R/\mathrm{Jac}(R))=0$ for Dedekind domain $R$ with $\mathrm{Jac}(R)\neq 0$?

Krull dimension of the ring $K[t^{-1},t]$

When is $\dim R_f = \dim R$?

Example of a Noetherian local ring of dimension one which is not a discrete valuation ring.

$\mu_R(m)\geq \dim R$ where $\mu_R(m)=\operatorname{embdim}R$.

Find dimension and depth of $R=S_{P}/[(x,y)\cap (z,w)]S_{P}$

Koszul applied to dimension theory

Final step of exercise 11.7 from Atiyah-Macdonald ($\dim A[x]=\dim A+1$)

Dimension formula

Give an example of ring that has two maximal chains of prime ideals of different lengths.

Dimension of a product of projective varieties

Computing $\dim (\mathbb{Q} + x \mathbb{R}[x])$

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