On the Stability of Graded Rings Original Research Article

Let R = circled plusnset membership, variantimageRn be a left Noetherian, left graded regular image-graded ring (i.e., every finitely generated graded R-module has finite projective dimension). We prove that if every finitely generated graded projective R-module is graded stably free then every finitely 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.