List questions from dimension-theory-algebra

Published on 25 Mar 2026 - 16:08

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About Hartshorne's Proposition 1.10

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187

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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 $n-r$.

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273

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

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1.3k

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

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6.8k

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

Published on 25 Mar 2026 - 16:12

637

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Hilbert function of ideal generated by linear forms.

Published on 25 Mar 2026 - 16:07

379

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

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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 25 Mar 2026 - 16:09

3k

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The height of a principal prime ideal

Published on 25 Mar 2026 - 16:08

333

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Which definition of dimension came first?

Published on 25 Mar 2026 - 16:12

1.4k

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

Published on 25 Mar 2026 - 16:08

138

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Injective endomorphism and Hilbert dimension

Published on 25 Mar 2026 - 16:07

673

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

Published on 25 Mar 2026 - 16:08

2.4k

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Krull dimension in polynomial rings

Published on 25 Mar 2026 - 16:08

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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