Abstract:The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.
Keywords: complete lattices, completely distributive lattices, Galois connection, multiplicative elements, way-below relation
AMS Subject Classification: 06A15, 06B35, 06D10