List questions from krull-dimension

Published on 26 Mar 2026 - 9:26

574

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What is the Krull dimension of a polynomial ring over a PID?

Published on 02 Mar 2021 - 20:22

192

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Krull Dimension of Affine Curve / Transcendence Degree of Coordinate Ring

Published on 23 Feb 2026 - 4:41

343

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$R[x]$ has Krull dimension 2 if $R$ is a PID

Published on 20 Mar 2021 - 12:05

110

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Dimension of the associated graded module at an ideal

Published on 26 Mar 2026 - 16:06

164

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Using Krull Dimension, show that the transcendence degree of an affine $K$-domain is the size of a maximal algebraically independent subset

Published on 28 Mar 2021 - 6:35

566

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Dimension of a scheme $X$ at a closed point $x$ and dimension of its local ring.

Published on 29 Mar 2026 - 8:15

219

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Classification of commutative rings $R$ satisfying $\dim(R[T])=\dim(R)+1$

Published on 29 Mar 2026 - 6:33

132

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equality of support of a module and its quotient

Published on 26 Mar 2026 - 4:34

115

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Krull dimension of $K[x,y]/\langle x^3,x^2-y^2,xy\rangle$

Published on 04 Jun 2021 - 16:40

207

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Inequality of the dimension of the formal power series ring when the ring is non-noetherian

Published on 04 Jun 2021 - 21:37

292

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Proving $\dim (R[[X]]) = \dim (R) + 1$ by using Krull's Principal Ideal Theorem, $R$ noetherian

Published on 16 Jun 2021 - 15:00

208

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A question about Dimension Theory of Noetherian Rings

Published on 20 Jun 2021 - 23:10

66

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Krull Dimension is defined by induction on ordinals.

Published on 27 Jun 2021 - 15:07

239

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Height of irreducible polynomials

Published on 29 Jun 2021 - 10:01

List Question

Can dimension of manifolds be understood similarly to dimension of schemes?

What is the Krull dimension of a polynomial ring over a PID?

Krull Dimension of Affine Curve / Transcendence Degree of Coordinate Ring

$R[x]$ has Krull dimension 2 if $R$ is a PID

Dimension of the associated graded module at an ideal

Using Krull Dimension, show that the transcendence degree of an affine $K$-domain is the size of a maximal algebraically independent subset

Dimension of a scheme $X$ at a closed point $x$ and dimension of its local ring.

Classification of commutative rings $R$ satisfying $\dim(R[T])=\dim(R)+1$

equality of support of a module and its quotient

Krull dimension of $K[x,y]/\langle x^3,x^2-y^2,xy\rangle$

Inequality of the dimension of the formal power series ring when the ring is non-noetherian

Proving $\dim (R[[X]]) = \dim (R) + 1$ by using Krull's Principal Ideal Theorem, $R$ noetherian

A question about Dimension Theory of Noetherian Rings

Krull Dimension is defined by induction on ordinals.

Height of irreducible polynomials

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