On the integral closure of ideals

Details On the integral closure of ideals On the integral closure of ideals

2002-10-15

arxiv.org/abs/math/0210229v1

Manu. Math. 95 (1998), 2689-2708

Mathematics

Commutative Algebra

15 pages

Scientific paper

Among the several types of closures of an ideal $I$ that have been defined and studied in the past decades, the integral closure $\bar{I}$ has a central place being one of the earliest and most relevant. Despite this role, it is often a difficult challenge to describe it concretely once the generators of $I$ are known. Our aim in this note is to show that in a broad class of ideals their radicals play a fundamental role in testing for integral closedness, and in case $I\neq \bar{I}$, $\surd{I}$ is still helpful in finding some fresh new elements in $\bar{I}\setminus I$. Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection ideals, and generically Gorenstein ideals.

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