List questions from krull-dimension

Published on 26 Mar 2026 - 4:34

70

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Prove the Krull dimension of coordinate ring of $y^2=x^3$ is $1$.

Published on 19 Oct 2019 - 14:22

235

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Regularity of localisation of a polynomial ring.

Published on 22 Mar 2026 - 17:14

104

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$f(x_1,x_2)\in k[x_1,x_2]$ - prove that $\dim Z(f)=1$

Published on 29 Nov 2019 - 16:41

279

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Krull dimension of polynomial ring in countably many variables

Published on 25 Mar 2026 - 17:26

139

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Dimension of the power series ring localized at its variables

Published on 26 Mar 2026 - 3:06

83

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$\dim Z(x_1x_2,x_2x_3,x_1x_3)=0$?

Published on 25 Mar 2026 - 20:41

156

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Krull dimension of the adele ring

Published on 11 Mar 2026 - 5:56

160

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Let $A$ be a Noetherian domain of dimension 1 with infinitely many maximal ideals. Let $f \in A[y]$. Show that $(f)$ is not a maximal ideal of $A[y]$.

Published on 26 Mar 2026 - 6:23

391

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Transcendence degree and Krull dimension of finitely generated algebras

Published on 23 Feb 2026 - 2:40

526

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Open nonempty subset of irreducible variety over $k$ has the same Krull dimension as the whole variety?

Published on 13 Jan 2020 - 18:25

263

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Is the ring of functions of an elliptic curve a UFD?

Published on 25 Mar 2026 - 21:50

58

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Krull dimension in quotient of local regular ring

Published on 25 Feb 2020 - 17:04

152

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On comparing dimension of $(0:_M I)$ and $M/IM$

Published on 08 Mar 2020 - 4:00

420

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Proof verification: determining the dimension of a polynomial ring from the going up theorem.

Published on 25 Mar 2026 - 7:43

List Question

Examples of 1 dimensional Noetherian rings that aren't domains

Prove the Krull dimension of coordinate ring of $y^2=x^3$ is $1$.

Regularity of localisation of a polynomial ring.

$f(x_1,x_2)\in k[x_1,x_2]$ - prove that $\dim Z(f)=1$

Krull dimension of polynomial ring in countably many variables

Dimension of the power series ring localized at its variables

$\dim Z(x_1x_2,x_2x_3,x_1x_3)=0$?

Krull dimension of the adele ring

Let $A$ be a Noetherian domain of dimension 1 with infinitely many maximal ideals. Let $f \in A[y]$. Show that $(f)$ is not a maximal ideal of $A[y]$.

Transcendence degree and Krull dimension of finitely generated algebras

Open nonempty subset of irreducible variety over $k$ has the same Krull dimension as the whole variety?

Is the ring of functions of an elliptic curve a UFD?

Krull dimension in quotient of local regular ring

On comparing dimension of $(0:_M I)$ and $M/IM$

Proof verification: determining the dimension of a polynomial ring from the going up theorem.

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