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Piggybacking Over Unbounded Distributive Lattices
Leonardo M. Cabrer and Hilary A. Priestley
This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-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.
Keywords: Distributive lattice, Priestley duality, natural duality, multisorted duality, piggyback method, Sugihara algebra
2010 Mathematics Subject Classification. Primary: 08C20; Secondary: 03G25, 06D50