TY - JOUR
T1 - On the integral closure of ideals
AU - Corso, Alberto
AU - Huneke, Craig
AU - Vasconcelos, Wolmer V.
PY - 1998/3
Y1 - 1998/3
N2 - Among the several types of closures of an ideal I that have been defined and studied in the past decades, the integral closure Ī 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 ≠ Ī, √I is still helpful in finding some fresh new elements in Ī\I. Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection ideals, and generically Gorenstein ideals.
AB - Among the several types of closures of an ideal I that have been defined and studied in the past decades, the integral closure Ī 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 ≠ Ī, √I is still helpful in finding some fresh new elements in Ī\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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U2 - 10.1007/s002290050033
DO - 10.1007/s002290050033
M3 - Article
AN - SCOPUS:0032008599
SN - 0025-2611
VL - 95
SP - 331
EP - 347
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 3
ER -