Question

Dimension of localization

score 442 · Answer 1 · 2026-03-25 11:09:31

442

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Dimension of localization

Published on 25 Mar 2026 - 11:09

score 233 · Answer 2 · 2017-02-25 06:48:58

233

Views

Example of a commutative noetherian ring with $1$ which is neither domain nor local and has a principal prime ideal of height $1.$

Published on 25 Feb 2017 - 6:48

score 120 · Answer 3 · 2023-01-29 20:47:44

120

Views

Proof that the Krull dimension of a ring R equals the dimension of Spec(R)

Published on 29 Jan 2023 - 20:47

score 102 · Answer 4 · 2023-02-03 01:16:40

102

Views

Calculating dimension of a tensor product of algebras

Published on 03 Feb 2023 - 1:16

score 46 · Answer 5 · 2026-03-25 06:04:12

46

Views

General method of finding dimension of a ring and determining regularity

Published on 25 Mar 2026 - 6:04

score 117 · Answer 6 · 2026-03-25 14:05:27

117

Views

Independence complex of a prime ideal is a matroid

Published on 25 Mar 2026 - 14:05

score 135 · Answer 7 · 2026-03-26 06:08:07

135

Views

On the height of the Jacobian ideal of the determinant of a square matrix of variables

Published on 26 Mar 2026 - 6:08

score 46 · Answer 8 · 2023-04-08 21:31:28

46

Views

Principal Ideal Theorem and geometric interpretation (Kempf 2.6.3)

Published on 08 Apr 2023 - 21:31

score 204 · Answer 9 · 2026-03-26 19:20:06

204

Views

Show that $K[x_1,x_2,x_3,x_4] / \langle x_1x_4 - x_2x_3 \rangle$ is an integral domain of dimension $3$

Published on 26 Mar 2026 - 19:20

score 138 · Answer 10 · 2023-06-01 12:08:44

138

Views

A complex affinie variety of dimension $\ge 1$ is never compact in the classical (Euclidean) topology

Published on 01 Jun 2023 - 12:08

score 49 · Answer 11 · 2026-03-25 23:34:49

49

Views

Find $S$ whith Krull $\dim S = 0$ such that $HS(S,\lambda) = 1 +3\lambda +5\lambda^2 +2\lambda^3 +\lambda^4$

Published on 25 Mar 2026 - 23:34

score 63 · Answer 12 · 2026-03-26 08:31:17

63

Views

Dimension of a positively graded ring after a suitable localization

Published on 26 Mar 2026 - 8:31

score 104 · Answer 13 · 2026-03-26 09:19:40

104

Views

Finding $I(V)$ for $V = V(x^2 + y^2 - z^2, 2z^2 - y)$

Published on 26 Mar 2026 - 9:19

score 64 · Answer 14 · 2023-06-28 21:17:19

64

Views

$\dim(A/a) \le \dim A - 1$ for domains $A$

Published on 28 Jun 2023 - 21:17

score 99 · Answer 15 · 2023-06-30 17:09:56

99

Views

Is there a short proof that the Krull dimension of $k[x_1, \dots,x_n]$ is $n$ using dimension theory?

Published on 30 Jun 2023 - 17:09

List Question

Dimension of localization

Example of a commutative noetherian ring with $1$ which is neither domain nor local and has a principal prime ideal of height $1.$

Proof that the Krull dimension of a ring R equals the dimension of Spec(R)

Calculating dimension of a tensor product of algebras

General method of finding dimension of a ring and determining regularity

Independence complex of a prime ideal is a matroid

On the height of the Jacobian ideal of the determinant of a square matrix of variables

Principal Ideal Theorem and geometric interpretation (Kempf 2.6.3)

Show that $K[x_1,x_2,x_3,x_4] / \langle x_1x_4 - x_2x_3 \rangle$ is an integral domain of dimension $3$

A complex affinie variety of dimension $\ge 1$ is never compact in the classical (Euclidean) topology

Find $S$ whith Krull $\dim S = 0$ such that $HS(S,\lambda) = 1 +3\lambda +5\lambda^2 +2\lambda^3 +\lambda^4$

Dimension of a positively graded ring after a suitable localization

Finding $I(V)$ for $V = V(x^2 + y^2 - z^2, 2z^2 - y)$

$\dim(A/a) \le \dim A - 1$ for domains $A$

Is there a short proof that the Krull dimension of $k[x_1, \dots,x_n]$ is $n$ using dimension theory?

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