Abstract
This paper shows that if (R,m) is a Nœtherian 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 Rˆ and the number of maximal ideals in S in the case when R is a Nœtherian quasi-unmixed local domain such that S is finite over R and Snˆ has only one minimal prime for all the maximal ideals n in S, where Snˆ is the n-adic completion of Sn.