List questions from monomial-ideals

Published on 03 May 2026 - 23:55

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Finite set of generators of monomial ideal form Gröbner basis

Published on 29 Apr 2026 - 12:52

93

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Prove $\langle x \rangle + \cap P_i = \cap (\langle x \rangle + P_i)$ for monomials ideals.

Published on 25 Apr 2026 - 18:14

386

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If the initial monomial ideal $in_<(I)$ is square free, then $I$ is a radical ideal.

Published on 04 May 2026 - 11:21

166

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Let $I = (X,Y) \subset k[X,Y]$ then $\dim_k(k[X,Y]/I^n) = \frac{n(n+1)}{2}$

Published on 10 May 2026 - 13:22

98

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Monomial ideal which is not saturated.

Published on 04 May 2026 - 12:58

186

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Reduces to $0$ of $S$-polynomial.

Published on 04 May 2026 - 6:59

58

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Showing $I:\langle v_j \rangle \subseteq \langle \{ u_i / \gcd(u_i,v_j) \ : \ i=1,\dots, r \} \rangle$, where $I=\langle u_1, \dots, u_r \rangle$

Published on 04 May 2026 - 12:03

137

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Assuming that $I,J\subset S$ are monomial ideals, is it true that $I+J$ is monomial? What about $IJ$ and $I\cap J$?

Published on 05 May 2026 - 14:31

160

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Complete Intersection ideal whose initial ideal is not even Cohen-Macaulay

Published on 04 May 2026 - 10:29

115

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Complete Intersection ideal for which $\mbox{in}_<(I)$ is not even Cohen-Macaulay

Published on 10 May 2026 - 12:33

266

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Quotient of monomial ideals

Published on 10 May 2026 - 12:32

118

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A question about initial ideals.

Published on 10 May 2026 - 12:30

116

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On monomial ideals and ring generated by monomials

Published on 10 May 2026 - 13:47

368

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On a colon ideal in the polynomial ring $\mathbb R[x,y]$

Published on 10 May 2026 - 12:34

List Question

Monomial ideal; Dickson's lemma

Finite set of generators of monomial ideal form Gröbner basis

Prove $\langle x \rangle + \cap P_i = \cap (\langle x \rangle + P_i)$ for monomials ideals.

If the initial monomial ideal $in_<(I)$ is square free, then $I$ is a radical ideal.

Let $I = (X,Y) \subset k[X,Y]$ then $\dim_k(k[X,Y]/I^n) = \frac{n(n+1)}{2}$

Monomial ideal which is not saturated.

Reduces to $0$ of $S$-polynomial.

Showing $I:\langle v_j \rangle \subseteq \langle \{ u_i / \gcd(u_i,v_j) \ : \ i=1,\dots, r \} \rangle$, where $I=\langle u_1, \dots, u_r \rangle$

Assuming that $I,J\subset S$ are monomial ideals, is it true that $I+J$ is monomial? What about $IJ$ and $I\cap J$?

Complete Intersection ideal whose initial ideal is not even Cohen-Macaulay

Complete Intersection ideal for which $\mbox{in}_<(I)$ is not even Cohen-Macaulay

Quotient of monomial ideals

A question about initial ideals.

On monomial ideals and ring generated by monomials

On a colon ideal in the polynomial ring $\mathbb R[x,y]$

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