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.
Publié le : 2001-07-05
Classification:
direct limit,
maximal semilattice quotient,
compact congruence,
real rank zero,
C*-algebra,
approximately finite dimensional,
von Neumann regular ring,
complemented modular lattice,
dimension group,
Distributive semilattice,
06A12, 06C20, 06F20, 16E20, 16E50, 19A49, 19K14, 46L05,
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]
@article{hal-00004050,
author = {Goodearl, Ken and Wehrung, Friedrich},
title = {Representations of distributive semilattices in ideal lattices of various algebraic structures},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00004050}
}
Goodearl, Ken; Wehrung, Friedrich. Representations of distributive semilattices in ideal lattices of various algebraic structures. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00004050/