Sequences and Ker(R[X1,…,Xg] → R[tl]) Original Research Article

Let I = (b1,…,bg)R (g ≥ 2) be an ideal in a Noetherian ring R, let K be the kernel of the natural homomorphism from Rg = R[X1,…,Xg] onto S = R[tI] (the restricted Rees ring of R with respect to I), and let J = ({biXj − bjXi; 1 ≤ i < j ≤ g})Rg. Then the main results in this paper strengthen two known results in the literature by showing: if b1,…,bg is a regular sequence, then K = J and, for all n ≥ 1, Ass(Rg/Jn) = Ass(Rg/K); and, if b1,…,bg is an asymptotic sequence, then Ka = Ja and, for all n ≥ 1, Ass(Rg/(Jn)a) = Ass(Rg/Ka) = {P;P is a minimal prime divisor of K}, where La denotes the integral closure of the ideal L.