Representations of distributive semilattices in ideal lattices of various algebraic structures

Ken Goodearl (1) , Friedrich Wehrung (2)

1 MATH-UCSB - Department of Mathematics [Santa Barbara]
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: 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

Domaines: Mathématiques générales [math.GM]

Ken Goodearl, Friedrich Wehrung. Representations of distributive semilattices in ideal lattices of various algebraic structures. Algebra Universalis, 2001, 45, pp.71-102. ⟨10.1007/s000120050203⟩. ⟨hal-00004050⟩