SEQUENCES AND KER(R[X-1,...,X-G]-]R[TI])

Let I = (b(1),...,b(g))R (g greater than or equal to 2) be an ideal in a Noetherian ring R, let K be the kernel of the natural homomorphism from R-g = R[X-1,...,X-g] onto S = R[tI] (the restricted Rees ring of R with respect to I), and let J = ({b(i)X(j)-b(j)X(i); 1 less than or equal to i < j less than or equal to g})R-g. Then the main results in this paper strengthen two known results in the literature by showing: if bl,...,b, is a regular sequence, then K = J and, for all n greater than or equal to 1,Ass(R-g/J(n)) = Ass(R-g/K); and, if b(1),...,b(g) i s an asymptotic sequence, then K-a = J(a) and, for all n greater than or equal to 1, Ass(R-g/(J(n))(a)) = Ass (R-g/K-a) = {P;P is a minimal prime divisor of K}, where L-a denotes the integral closure of the ide al L. (C) 1997 Elsevier Science B.V.