Mathematics – Commutative Algebra
Scientific paper
2008-01-22
Mathematics
Commutative Algebra
revised version, references added, to appear in Math. Z
Scientific paper
In two dimensional regular local rings integrally closed ideals have a unique factorization property and have a Cohen-Macaulay associated graded ring. In higher dimension these properties do not hold for general integrally closed ideals and the goal of the paper is to identify a subclass of integrally closed ideals for which they do. We restrict our attention to 0-dimensional homogeneous ideals in polynomial rings $R$ of arbitrary dimension and identify a class of integrally closed ideals, the Goto-class $\G^*$, that is closed under product and that has a suitable unique factorization property. Ideals in $\G^*$ have a Cohen-Macaulay associated graded ring if either they are monomial or $\dim R\leq 3$. Our approach is based on the study of the relationship between the notions of integrally closed, contracted, full and componentwise linear ideals.
Conca Aldo
Negri Emanuela de
Rossi Maria Evelina
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