# Questions tagged [monomial-ideals]

Use this tag for question involving monomial ideals in polynomial rings of several variables over a commutative ring. This tag should be used together with the tag of commutative algebra.

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### On the definition of Chow rings for atomic lattices

In the following paper https://arxiv.org/pdf/math/0305142.pdf the authors introduce an algebra $D(\mathcal{L},\mathcal{G})$ (see Definition 3). However, they assert that "although D is defined ...
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### Permutation of index and permutation of vector of powers of monomial

I am confused about the following easy stuff, Let $$\mathbf{x} =\begin{bmatrix} x_1 & \cdots & x_n\end{bmatrix}^T .$$ Suppose I have the following monomial \mathbf{x}^{\alpha}=x^{\alpha_1}...
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### On monomial ideals and ring generated by monomials

Question 1: Is $(x^4,x^3y,x^2y^2,xy^3,y^4)$ a maximal ideal in $\mathbb C [ x^4,x^3y,x^2y^2,xy^3,y^4]$? Question 2: Are the ideals $(x^4,x^3y,x^2y^2,xy^3,y^4)$ and $(x^4,x^3y,xy^3,y^4)$ distinct in ...
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### A question about initial ideals.

Let $R = k[x_1, \dots, x_m]$ be a polynomial ring over a field $k$ and $I, J$ be ideals of $R$. Further assume that $J$ is generated by the polynomials $f_1, \dots, f_r$. Fix a monomial order $<$ ...
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