Representation Theorems For Some Ordered Algebraic Structures

Abstract

In this thesis, we extended Priestley's classical results by proving a representation theorem within the framework for algebraic structures of bounded distributive hyperlattice and negatively ordered commutative monoids. We establish categorical equivalence between the dual of Priestley spaces equipped with negatively ordered commutative semigroups and the category of bounded distributive hyperlattice with negatively ordered commutative monoids. Furthermore, this research establishes a Priestley-style duality between the category of bounded distributive hyperlattices endowed with a negatively ordered commutative hypermonoid structure and the category of Priestley spaces associated with negatively ordered commutative semihypergroups, in order to establish categorical equivalence between them.