K<inf>0</inf> of purely infinite simple regular rings

P. Ara, K. R. Goodearl, E. Pardo

Research output: Contribution to journalArticleResearchpeer-review

63 Citations (Scopus)

Abstract

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-theory. For instance, if R is a purely infinite simple ring, then K0(R)+ = K0(R),the monoid of isomorphism classes of finitely generated projective R-modules is isomorphic to the monoid obtained from K0(R) by adjoining a new zero element, and K 1(R) is the Abelianization of the group of units of R. We develop techniques of construction, obtaining new examples in this class in the case of von Neumann regular rings, and we compute the Grothendieck groups of these examples. In particular, we prove that every countable Abelian group is isomorphic to K0 of some purely infinite simple regular ring. Finally, some known examples are analyzed within this framework. © 2002 Kluwer Academic Publishers.
Original languageEnglish
Pages (from-to)69-100
JournalK-Theory
Volume26
DOIs
Publication statusPublished - 1 Dec 2002

Keywords

  • Grothendieck group
  • Purely infinite simple ring
  • Universal localization
  • Von Neumann regular ring

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