Projective equivalence of ideals in Noetherian integral domains

Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive integer m such that all the Rees integers of IA are equal to m. Moreover, if R has altitude one, then all the Rees integers of J=Rad(IA) are equal to one and the ideals Jm and IA have the same integral closure. Thus Rad(IA)=J is a projectively full radical ideal that is projectively equivalent to IA. In particular, if R is Dedekind, then there exists a Dedekind domain A having the following properties: (i) A is a finite separable integral extension of R; and (ii) there exists a radical ideal J of A and a positive integer m such that IA=Jm. In this case the extension A also has the property that for each maximal ideal N of A with I⊆N, the canonical inclusion R/(N∩R)↪A/N is an isomorphism, and the integer m is a multiple of [A(0):R(0)].