The algebraic \(K\)-theory of operator algebras
The author studies the algebraic \(K\)-theory of \(C^*\)-algebras, i.e., when the algebras are considered purely algebraically as rings, forgetting the topology. It is proved that commutative \(C^*\)-algebras are \(K\)-regular in all degrees, that is, all their \(N^r K_i\)-groups vanish. Extensions and generalizations of the Fischer--Prasolov theorem comparing algebraic and topological \(K\)-theory with finite coefficients are given. Polynomial rings over commutative \(C^*\)-algebras are studied.
scientific article; zbMATH DE number 1059652