Prime divisors of powers of ideals in some Laskerian rings

AbstractLet R be a Noetherian domain. Let I be a nonzero proper ideal of R such that for all prime ideals Q associated to the ideal I, the associated graded ring of R with respect to Q is an integral domain. Let S be a subring of R such that I is contained in S and S/I is a zero-dimensional Laskerian ring. Then for any proper ideal B of S there exists a positive integer ‘m’ depending on B, such that the set of associated prime ideals of Bn for any n ≥ m equals the set of associated prime ideals of Bm