Representations of distributive semilattices in ideal lattices of various algebraic structures

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.

To appear in Algebra Universalis. Former title: "Representations of distributive semilattices by dimension groups, regular rings, C*-algebras and complemented modular lattices"