This project will investigate the relationship between the theory of locales and the theory of ideals. The principal investigators will examine the interplay of ring theory and topology as it relates to spatiality of sublocales and prime decompositions; closure and coclosure operators on closed posets; localization; and the development of the theory of modules over a closed poset. The proposed research is in the area of general algebra. It concerns a study of partially ordered algebraic structures with the hope of clarifying algebraic and lattice theoretic aspects of ring theory and topos theory.
