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algebra universalis

, Volume 45, Issue 1, pp 71–102 | Cite as

Representations of distributive semilattices in ideal lattices of various algebraic structures

  • K. R. Goodearl
  • F. Wehrung

Abstract.

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics.

Key words and phrases: Distributive semilattice, von Neumann regular ring, dimension group, complemented modular lattice, C*-algebra, approximately finite dimensional, direct limit, compact congruence, maximal semilattice quotient, real rank zero. 

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Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • K. R. Goodearl
    • 1
  • F. Wehrung
    • 2
  1. 1.Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, e-mail: goodearl@math.ucsb.edu, URL: http://www.math.ucsb.edu/~goodearlUS
  2. 2.CNRS, ESA 6081, Département de Mathématiques, Université de Caen, F-14032 Caen Cedex, France, e-mail: wehrung@math.unicaen.fr, URL: http://www.math.unicaen.fr/~wehrungFR

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