Product of distinct simple integrally closed ideals in 2-dimensional regular local rings

Abstract

Let (R, m) be a two-dimensional regular local ring and I an mprimary integrally closed ideal in R. In this paper, we give equivalent conditions for I to be a product of distinct simple m-primary integrally closed ideals (i.e., I = II ... Il, where II,, I are distinct simple m-primary integrally closed ideals of R) in terms of the regularity of R[It]/p for all p E Min(mR[It]) and in terms of how to choose a minimal generating set for I over its minimal reductions.