Weak normalization in graded extensions and weak subintegral closure of ideals

Abstract

We study several aspects of the weak normalization in a graded extension of commutative rings. Applied to the Rees algebra of an ideal in a noetherian ring, the results obtained allow us to prove several properties of the weak subintegral closure of an ideal, a concept introduced by Vitulli and Leahy. The same methods are also used to eliminate one of the hypotheses in a theorem of Gaffney and Vitulli.