XX.—A Coördinatisation of Lattices by One-sided Baer Assemblies
T. S. Blyth, William C. Hardy · Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences · 1972
Synopsis In an earlier publication [1] we introduced the notion of a Baer assembly and applied it to obtain a coördinatisation theory for semilattices. This was achieved by considering the semigroup of quasi-residuated (i.e. ℴ-preserving and isotone) mappings on a bounded semilattice. In the present paper we consider the semigroup of quasi-residuated ∪-homomorphisms (or hemimorphisms) on a bounded lattice and thus show how a particular type of one-sided Baer assembly can be used to provide a coördinatisation theory for lattices; and in particular for complemented, modular and distributive lattices.