On the integral closure of ideals

Among the several types of closures of an idealI that have been defined and studied in the past decades, the integral closureĪ 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 ofI 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 caseI ≠Ī, ✓I is still helpful in finding some fresh new elements inĪ/I. Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection ideals, and generically Gorenstein ideals. Part of the results contained in this paper were obtained while the first author was visiting Rutgers University and was partially supported by CNR grant 203.01.63, Italy. The second and third authors were partially supported by the NSF. This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag