Piggybacking over unbounded distributive lattices

Abstract

This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributivelattice-based algebras in which the lattice reducts are not assumed to have bounds. The development of theory to parallel what is known for the exhaustively-studied bounded case was initially driven by need. This arose in connection with a major investigation of Sugihara algebras and Sugihara monoids. The theorems in this paper apply in a systematic way to a range of examples: varieties of Sugihara type; other classes of algebras previously treated ad hoc; and further classes as required.