Refinement monoids with weak comparability and applications to regular rings and C*-algebras

Abstract

We prove a cancellation theorem for simple re nement monoids satisfying the weak comparability condition, rst introduced by K.C. O'Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and C -algebras of real rank zero via the monoid of isomorphism classes of nitely generated projective modules.