ON THE STABILITY OF GRADED RINGS

Let R = +n is-an-element-of ZR(n) be a left Noetherian, left graded re gular Z-graded ring (i.e., every finitely generated graded R-module ha s finite projective dimension). We prove that if every finitely genera ted graded projective R-module is graded stably free then every finite ly generated projective R-module is stably free. Some applications of this result to graded rings and Rees rings of Zariskian filtered rings are also given. (C) 1994 Academic Press, Inc.