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September, 2003 Integral Closure of Monomial Ideals on Regular Sequences
Karlheinz Kiyek, Jürgen Stückrad
Rev. Mat. Iberoamericana 19(2): 483-508 (September, 2003).


It is well known that the integral closure of a monomial ideal in a polynomial ring in a finite number of indeterminates over a field is a monomial ideal, again. Let $R$ be a noetherian ring, and let $(x_1,\ldots,x_d)$ be a regular sequence in $R$ which is contained in the Jacobson radical of $R$. An ideal $\mathfrak a$ of $R$ is called a monomial ideal with respect to $(x_1,\ldots,x_d)$ if it can be generated by monomials $x_1^{i_1}\cdots x_d^{i_d}$. If $x_1R+\cdots + x_dR$ is a radical ideal of $R$, then we show that the integral closure of a monomial ideal of $R$ is monomial, again. This result holds, in particular, for a regular local ring if $(x_1,\ldots,x_d)$ is a regular system of parameters of $R$.


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Karlheinz Kiyek. Jürgen Stückrad. "Integral Closure of Monomial Ideals on Regular Sequences." Rev. Mat. Iberoamericana 19 (2) 483 - 508, September, 2003.


Published: September, 2003
First available in Project Euclid: 8 September 2003

zbMATH: 1069.13005
MathSciNet: MR2023197

Primary: 13B22
Secondary: 13B25

Keywords: integral closure of monomial ideals , monomial ideals , regular sequences

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 2 • September, 2003
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