Ploščica, Miroslav Local separation in distributive semilattices. (English) Zbl 1086.06003 Algebra Univers. 54, No. 3, 323-335 (2005). Summary: We introduce the Local Separation Property (LSP) for distributive semilattices. We show that LSP holds in many semilattices of the form \(\text{Con}_c A\), where \(A\) is a lattice. On the other hand, we construct an abstract example of a distributive lattice without LSP. Our research is connected with the well-known open problem whether every distributive algebraic lattice is isomorphic to the congruence lattice of some lattice. Cited in 3 Documents MSC: 06A12 Semilattices 06B10 Lattice ideals, congruence relations 06D05 Structure and representation theory of distributive lattices 54H10 Topological representations of algebraic systems Keywords:refinement; local separation property; distributive semilattices; distributive lattice; congruence PDFBibTeX XMLCite \textit{M. Ploščica}, Algebra Univers. 54, No. 3, 323--335 (2005; Zbl 1086.06003) Full Text: DOI