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December, 2006 Asymptotic behaviour of monomial ideals on regular sequences
Monireh Sedghi
Rev. Mat. Iberoamericana 22(3): 955-962 (December, 2006).


Let $R$ be a commutative Noetherian ring, and let $\mathbf{x}= x_1, \ldots, x_d$ be a regular $R$-sequence contained in the Jacobson radical of $R$. An ideal $I$ of $R$ is said to be a monomial ideal with respect to $\mathbf{x}$ if it is generated by a set of monomials $x_1^{e_1}\ldots x_d^{e_d}$. The monomial closure of $I$, denoted by $\widetilde{I}$, is defined to be the ideal generated by the set of all monomials $m$ such that $m^n\in I^n$ for some $n\in \mathbb{N}$. It is shown that the sequences $\mathrm{Ass}_RR/\widetilde{I^n}$ and $\mathrm{Ass}_R\widetilde{I^n}/I^n$, $n=1,2, \ldots,$ of associated prime ideals are increasing and ultimately constant for large $n$. In addition, some results about the monomial ideals and their integral closures are included.


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Monireh Sedghi . "Asymptotic behaviour of monomial ideals on regular sequences." Rev. Mat. Iberoamericana 22 (3) 955 - 962, December, 2006.


Published: December, 2006
First available in Project Euclid: 22 January 2007

zbMATH: 1115.13016
MathSciNet: MR2320407

Primary: 13B20 , 13B21

Keywords: integral closures , monomial closures , monomial ideals

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.22 • No. 3 • December, 2006
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