Representations of distributive semilattices in ideal lattices of various algebraic structures

2000/11/13 by K. R. Goodearl, F. Wehrung
Mathematics · #math.OA #msc:06A12 #msc:06C20 #msc:06F20 #msc:16E20 #msc:16E50 #msc:19A49 #msc:19K14 #msc:46L05

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published as Algebra Universalis 45 (2001) 71--102 · To appear in Algebra Universalis. Former title: "Representations of distributive semilattices by dimension groups, regular rings, C*-algebras and complemented modular lattices"

arxiv created 2000/11/13 · arxiv updated 2009/11/30

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.

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