Question

Tower of integral extensions

score 150 · Answer 1 · 2026-03-26 22:51:57

150

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Tower of integral extensions

Published on 26 Mar 2026 - 22:51

score 84 · Answer 2 · 2026-03-24 23:45:59

84

Views

Does there exist a $1$-dimensional Noetherian domain whose set of all prime ideals has cardinality $\aleph_1$ ?

Published on 24 Mar 2026 - 23:45

score 361 · Answer 3 · 2026-03-25 09:02:33

361

Views

On "homogeneous" height and "homogeneous" Krull-dimension?

Published on 25 Mar 2026 - 9:02

score 281 · Answer 4 · 2026-03-23 12:10:41

281

Views

Dimension of the tangent cone of $V(\mathfrak{a})$

Published on 23 Mar 2026 - 12:10

score 443 · Answer 5 · 2026-03-22 20:46:50

443

Views

$B \subseteq A$ be an integral extension of integral domains where $B$ is normal; if $P \in Spec A$ and $Q=P\cap B$, then $\dim A_P=\dim B_Q$?

Published on 22 Mar 2026 - 20:46

score 51 · Answer 6 · 2026-03-25 03:02:55

51

Views

Showing that the Krull dimension of a certain domain is 1.

Published on 25 Mar 2026 - 3:02

score 78 · Answer 7 · 2018-05-20 04:51:51

78

Views

$R$ a commutative ring of characteristic $n>0$. If there is a monic polynomial in $(\mathbb Z/n)[X]$ vanishing identically on $R$, then $\dim R=0$

Published on 20 May 2018 - 4:51

score 723 · Answer 8 · 2018-05-20 14:13:16

723

Views

Computing Krull dimension of $\mathbb{K}[X,Y]/ (XY+X^2+Y^3)$

Published on 20 May 2018 - 14:13

score 105 · Answer 9 · 2018-06-05 01:22:27

105

Views

Dimension of irreducible components in polynomial ring

Published on 05 Jun 2018 - 1:22

score 134 · Answer 10 · 2026-03-25 01:43:11

134

Views

Valuation ring whose unique maximal ideal and every ideal of finite height is principal

Published on 25 Mar 2026 - 1:43

score 63 · Answer 11 · 2026-03-22 15:00:34

63

Views

$\dim R$=$\sup\{\dim R_f|f\in R\}$

Published on 22 Mar 2026 - 15:00

score 39 · Answer 12 · 2026-03-25 21:49:59

39

Views

Given prime ideals $\mathfrak p_A,\mathfrak p_B$ of commutative rings $A,B$ respectively, to determine $ht(\mathfrak p_A \times \mathfrak p_B)$

Published on 25 Mar 2026 - 21:49

score 138 · Answer 13 · 2026-03-25 12:24:56

138

Views

Valuation ring of finite Krull dimension whose every non-maximal ideal is principal

Published on 25 Mar 2026 - 12:24

score 198 · Answer 14 · 2026-03-20 16:35:04

198

Views

Example of Gorenstein ring that has infinite Krull dimension?

Published on 20 Mar 2026 - 16:35

score 228 · Answer 15 · 2026-03-25 21:51:15

228

Views

Intersection of all positive powers of a prime ideal in integral domain with all ideals of finite height

Published on 25 Mar 2026 - 21:51

List Question

Tower of integral extensions

Does there exist a $1$-dimensional Noetherian domain whose set of all prime ideals has cardinality $\aleph_1$ ?

On "homogeneous" height and "homogeneous" Krull-dimension?

Dimension of the tangent cone of $V(\mathfrak{a})$

$B \subseteq A$ be an integral extension of integral domains where $B$ is normal; if $P \in Spec A$ and $Q=P\cap B$, then $\dim A_P=\dim B_Q$?

Showing that the Krull dimension of a certain domain is 1.

$R$ a commutative ring of characteristic $n>0$. If there is a monic polynomial in $(\mathbb Z/n)[X]$ vanishing identically on $R$, then $\dim R=0$

Computing Krull dimension of $\mathbb{K}[X,Y]/ (XY+X^2+Y^3)$

Dimension of irreducible components in polynomial ring

Valuation ring whose unique maximal ideal and every ideal of finite height is principal

$\dim R$=$\sup\{\dim R_f|f\in R\}$

Given prime ideals $\mathfrak p_A,\mathfrak p_B$ of commutative rings $A,B$ respectively, to determine $ht(\mathfrak p_A \times \mathfrak p_B)$

Valuation ring of finite Krull dimension whose every non-maximal ideal is principal

Example of Gorenstein ring that has infinite Krull dimension?

Intersection of all positive powers of a prime ideal in integral domain with all ideals of finite height

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