ON THE INTEGRAL CLOSURE OF IDEALS

Among the several types of closures of an Ideal I that have been defin ed and studied in the past decades, the integral closure (I) over bar has a central place being one of the earliest and most relevant. Despi te this role, it is often a difficult challenge to describe it concret ely once the generators of I are known. Our aim in this note is to sho w that in a broad class of ideals their radicals play a fundamental ro le in testing for integral closedness, and in case I not equal (I) ove r bar, root I is still helpful in finding some fresh new elements in ( I) over bar\I, Among the classes of ideals under consideration are: co mplete intersection ideals of codimension two, generic complete inters ection ideals, and generically Gorenstein ideals.