List questions from monomial-ideals

Published on 22 Mar 2026 - 17:36

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Finite set of generators of monomial ideal form Gröbner basis

Published on 23 Mar 2026 - 9:51

88

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

Published on 20 Mar 2026 - 1:58

380

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

Published on 22 Mar 2026 - 20:31

159

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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 22 Mar 2026 - 22:21

90

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Monomial ideal which is not saturated.

Published on 23 Mar 2026 - 7:06

179

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

Published on 22 Mar 2026 - 13:20

52

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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 23 Mar 2026 - 9:24

132

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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 22 Mar 2026 - 10:29

153

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

Published on 23 Mar 2026 - 6:27

110

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

Published on 25 Mar 2026 - 2:45

262

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Quotient of monomial ideals

Published on 25 Mar 2026 - 3:00

113

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A question about initial ideals.

Published on 25 Mar 2026 - 7:38

112

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On monomial ideals and ring generated by monomials

Published on 25 Mar 2026 - 2:59

364

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

Published on 25 Mar 2026 - 4:39

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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