Duality for bounded distributive hyperlattice negatively ordered commutative monoids [Articol]

Abstract

The aim of this paper is to prove the Priestley representation theorem for bounded distributive lattices in the framework of bounded distributive hyperlattice negatively ordered commutative monoids. In this way, some results of Priestley’s work are extended. In particular, we show that the dual of the category of Priestley spaces negatively ordered commutative semigroups is equivalent to the category of bounded distributive hyperattice negatively ordered commutative monoids.