Some results on quasi-unmixed local domains

Abstract

Available online xxxx Communicated by Steven Dale Cutkosky MSC: 13B35 13B22 13A18 Keywords: Divisorial valuations Quasi-unmixed local domainsThis paper shows that if (R, m) is a Noetherian unibranch local domain with field of fractions K, then the integral closure S of R in K is analytically irreducible and finite over R if and only if R is analytically irreducible. We also prove the equality between the number of minimal prime ideals in R and the number of maximal ideals in S in the case when R is a Noetherian quasi-unmixed local domain such that S is finite over R and S n has only one minimal prime for all the maximal ideals n in S, where S n is the n-adic completion of S n .