Rational \(C^*\)-algebras and nonstable K-theory
The aim of this paper is to give some aspects of comparison theory for idempotents or finitely generated projective modules over unital rings, particularly over unital \(C^*\)-algebras. Namely several aspects of nonstable K-theory (that is the processes by which the K-theory data relate back to actual structure of the ring and its projective modules) are discussed, and some new relationships based on results in the theory of abelian semigroups are developed. These results are applied to solve nonstable K-theory problems for certain ``rationalized'' rings.
comparison theory for idempotents or finitely generated projective modules over unital rings
scientific article