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

Ara, P.; Pardo, E.

doi:10.1090/S0002-9939-96-03059-6

Refinement monoids with weak comparability and applications to regular rings and $C*$-algebras
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by P. Ara and E. Pardo PDF

Proc. Amer. Math. Soc. 124 (1996), 715-720 Request permission

Abstract:

We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first 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 finitely generated projective modules.

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