Abstract
In this paper, we will show that if (R, ) is a quasi-unmixed local ring, I an -primary ideal of R and ℛ (I) is the set of Rees valuations of I, then the number of minimal prime ideals in the -adic completion of R equals exactly the number of equivalence classes on the set ℛ (I) under the equivalence relation ∼defined by: ν
1
∼ ν
2
if there exist a constant c ≥ 1 such that for all x ∈ R, ν
1
(x) ≤ cν
2
(x) and ν
2
(x) ≤ cν
1
(x).