Integral closure and generic elements

Abstract

AbstractLet (R,m) be a formally equidimensional local ring with depthR⩾2 and I=(a1,…,an) an m-primary ideal in R. The main result of this paper shows that if I is integrally closed, then so is its image modulo a generic element, that is, if T=R[X1,…,Xn]/(a1X1+⋯+anXn), then IT¯=I¯T