Melvin F. Janowitz, R.C. Powers, T. Riedel
Primes, coprimes and multiplicative elements

Comment.Math.Univ.Carolinae 40,4 (1999) 607-615.

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