2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60328We 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"Operator Algebras06A12; 06C20; 06F20; 16E20; 16E50; 19A49; 19K14; 46L05 46L05text