Question

The Hilbert function and polynomial of $S = k[x_1, x_2, x_3, x_4]$ and $I = (x_1x_3, x_1x_4, x_2x_4)$ step clarification.

score 172 · Answer 1 · 2021-04-18 19:33:40

172

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The Hilbert function and polynomial of $S = k[x_1, x_2, x_3, x_4]$ and $I = (x_1x_3, x_1x_4, x_2x_4)$ step clarification.

Published on 18 Apr 2021 - 19:33

score 247 · Answer 2 · 2021-05-03 11:22:26

247

Views

The ideal $(x^5,y^6,xy)$ cannot be generated by two elements

Published on 03 May 2021 - 11:22

score 151 · Answer 3 · 2021-05-11 15:20:36

151

Views

Proving that $\langle LT(I) \rangle$ is a monomial ideal where $I$ is an ideal.

Published on 11 May 2021 - 15:20

score 43 · Answer 4 · 2021-05-22 15:39:52

43

Views

Let $J=\langle x,y\rangle$ and $I=J^3=J\cdot J\cdot J$ in $\mathbb{Q}[x,y]$. (Two questions down below in the body...)

Published on 22 May 2021 - 15:39

score 275 · Answer 5 · 2026-03-25 16:03:27

275

Views

About the height of primes associated to a squarefree monomial ideal $I\subseteq J$

Published on 25 Mar 2026 - 16:03

score 135 · Answer 6 · 2021-06-09 15:12:15

135

Views

Are minimal Groebner bases minimized bases?

Published on 09 Jun 2021 - 15:12

score 44 · Answer 7 · 2021-06-12 12:13:22

44

Views

a corollary of dickson's lemma!

Published on 12 Jun 2021 - 12:13

score 77 · Answer 8 · 2021-10-08 06:23:20

77

Views

Minimal prime ideals and associated prime ideals

Published on 08 Oct 2021 - 6:23

score 419 · Answer 9 · 2021-10-28 12:54:39

419

Views

Compute Intersection of Two Ideals

Published on 28 Oct 2021 - 12:54

score 186 · Answer 10 · 2021-11-07 15:42:24

186

Views

The intersection of squarefree monomial ideals is a squarefree monomial ideal

Published on 07 Nov 2021 - 15:42

score 88 · Answer 11 · 2022-01-24 12:24:12

88

Views

Castelnuovo-Mumford Regularity of Sub-ideals $I \subset J$

Published on 24 Jan 2022 - 12:24

score 91 · Answer 12 · 2022-03-07 04:29:52

91

Views

Betti number of graded ideal and graded quotients

Published on 07 Mar 2022 - 4:29

score 205 · Answer 13 · 2022-03-09 16:46:50

205

Views

Minimal generating set of a monomial ideal of $k[x_1,\dots,x_n]$

Published on 09 Mar 2022 - 16:46

score 179 · Answer 14 · 2022-04-30 10:40:45

179

Views

Monomial in monomial ideal

Published on 30 Apr 2022 - 10:40

score 325 · Answer 15 · 2026-03-21 20:55:36

325

Views

Example of initial ideal

Published on 21 Mar 2026 - 20:55

List Question

The Hilbert function and polynomial of $S = k[x_1, x_2, x_3, x_4]$ and $I = (x_1x_3, x_1x_4, x_2x_4)$ step clarification.

The ideal $(x^5,y^6,xy)$ cannot be generated by two elements

Proving that $\langle LT(I) \rangle$ is a monomial ideal where $I$ is an ideal.

Let $J=\langle x,y\rangle$ and $I=J^3=J\cdot J\cdot J$ in $\mathbb{Q}[x,y]$. (Two questions down below in the body...)

About the height of primes associated to a squarefree monomial ideal $I\subseteq J$

Are minimal Groebner bases minimized bases?

a corollary of dickson's lemma!

Minimal prime ideals and associated prime ideals

Compute Intersection of Two Ideals

The intersection of squarefree monomial ideals is a squarefree monomial ideal

Castelnuovo-Mumford Regularity of Sub-ideals $I \subset J$

Betti number of graded ideal and graded quotients

Minimal generating set of a monomial ideal of $k[x_1,\dots,x_n]$

Monomial in monomial ideal

Example of initial ideal

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