The algebraic \(K\)-theory of operator algebras
type: Item
instance of: scholarly article
title: The algebraic \(K\)-theory of operator algebras
zbMATH Open document ID: 0888.19004
DOI: 10.1023/A:1007736420938
published in: \(K\)-Theory
publication date: 1998-05-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 19K99
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 19D50
Mathematics Subject Classification ID: 19D35
Mathematics Subject Classification ID: 19L41
zbMATH DE Number: 1059652
zbMATH Keywords: \(C^*\)-algebras
zbMATH Keywords: algebraic \(K\)-theory
zbMATH Keywords: \(K\)-theory with finite coefficients
zbMATH Keywords: stable rank
author: Jonathan M. Rosenberg
MaRDI profile type: Publication
full work available at URL: a:1007736420938
OpenAlex ID: W2093820799
description: scientific article; zbMATH DE number 1059652