List questions from dimension-theory-algebra

Published on 08 Jun 2017 - 14:41

503

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About Hartshorne's Proposition 1.10

Published on 06 Sep 2017 - 17:16

186

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Prove that the transcendental degree of $k[x_1,\cdots, x_n]/(f_1,f_2,\cdots,f_r)$ is larger than $n-r$.

Published on 06 Nov 2017 - 23:20

272

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When do open affine subschemes of equidimensional schemes are again equidimensional?

Published on 15 Dec 2017 - 17:53

1.3k

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Proving that irreducible components of Zariski closed subsets are minimal prime ideals

Published on 19 Dec 2017 - 17:38

6.8k

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Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?

Published on 22 Mar 2026 - 14:02

636

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Hilbert function of ideal generated by linear forms.

Published on 22 Mar 2026 - 8:16

378

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On Krull dimension of $M/(0 :_{M} \mathfrak{m}^t)$ module

Published on 21 Mar 2026 - 9:19

4.5k

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Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left< x_1x_3-x_2^2,x_2 x_4-x_3^2,x_1x_4-x_2 x_3\right>$

Published on 21 Mar 2026 - 23:11

3k

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The height of a principal prime ideal

Published on 21 Mar 2026 - 19:39

332

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Which definition of dimension came first?

Published on 21 Mar 2026 - 21:42

1.4k

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Transcendence degree of $K[X_1,X_2,\ldots,X_n]$

Published on 22 Mar 2026 - 11:50

137

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Injective endomorphism and Hilbert dimension

Published on 22 Mar 2026 - 5:25

672

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Hilbert (polynomial) dimension and dimension of a support of a module

Published on 21 Mar 2026 - 21:17

2.4k

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Krull dimension in polynomial rings

Published on 22 Mar 2026 - 1:26

List Question

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

About Hartshorne's Proposition 1.10

Prove that the transcendental degree of $k[x_1,\cdots, x_n]/(f_1,f_2,\cdots,f_r)$ is larger than $n-r$.

When do open affine subschemes of equidimensional schemes are again equidimensional?

Proving that irreducible components of Zariski closed subsets are minimal prime ideals

Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?

Hilbert function of ideal generated by linear forms.

On Krull dimension of $M/(0 :_{M} \mathfrak{m}^t)$ module

Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left< x_1x_3-x_2^2,x_2 x_4-x_3^2,x_1x_4-x_2 x_3\right>$

The height of a principal prime ideal

Which definition of dimension came first?

Transcendence degree of $K[X_1,X_2,\ldots,X_n]$

Injective endomorphism and Hilbert dimension

Hilbert (polynomial) dimension and dimension of a support of a module

Krull dimension in polynomial rings

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