Finite generation of powers of ideals

Suppose M is a maximal ideal of a commutative integral domain R and that so me power M-n of M is finitely generated. We show that M is finitely generat ed in each of the following cases: (i) M is of height one, (ii) R is integr ally closed and ht M = 2, (iii) R = K[X; (S) over tilde] S] is a monoid dom ain over a field K, where (S) over tilde = S boolean OR {0} is a cancellati ve torsion-free monoid such that boolean AND(m=1)(infinity) mS = 0, and M i s the maximal ideal (X-s : s is an element of S). We extend the above resul ts to ideals I of a reduced ring R such that R/I is Noetherian. We prove th at a reduced ring R is Noetherian if each prime ideal of R has a power that is finitely generated. For each d with 3 less than or equal to d less than or equal to infinity, we establish existence of a d-dimensional integral d omain having a nonfinitely generated maximal ideal M of height d such that M-2 is 3-generated.