Priestley rings and Priestley order-compactifications (Q651431)

The authors study partially ordered sets by introducing the concept of Priestley rings of upsets. They prove that the family of non-equivalent Priestley ring representations of a distributive lattice can be put in bijection with the family of dense subspaces of the Priestley space of the given lattice. Furthermore, the authors also introduce the concept of Priestley order-compactifications as well as that of Priestley bases of an ordered topological space, proving that there are isomorphic. Classical results due to \textit{H. Bauer} [Arch. Math. 6, 215--222 (1955; Zbl 0065.03901)] and [\textit{Ph. Dwinger}, Introduction to Boolean algebras. Hamburger Mathematische Einzelschriften. 40. Heft. Würzburg: Physica-Verlag (1961; Zbl 0102.02502)] are generalized throughout the paper.