Topologically defined classes of going-down domains

Abstract

Let R be an integral domain. Our purpose is to study GD (going-down) domains which arise topologically; that is, we investigate how certain going-down assumptions on R and its overrings relate to the topological space Spec ( R ) {\text {Spec}}(R) . Many classes of GD domains are introduced topologically, and a systematic study of their behavior under homomorphic images, localization and globalization, integral change of rings, and the “ D + M D + M construction” is undertaken. Also studied, is the algebraic and topological relationships between these newly defined classes of GD domains.