On Chow Groups of G-Graded Rings

Abstract

Let A be a Noetherian ring graded by a finitely generated Abelian group G. It is shown that a Chow group A _?(A) of A is determined by cycles and a rational equivalence with respect to certain G-graded ideals of A. In particular, A _?(A) is isomorphic to the equivariant Chow group of A if G is torsion free.