Elements Weakly Prime and Weakly Primary to Another Element

Abstract

Let L be a compactly generated multiplicative lattice with 1 compact in which every finite product of compact elements is compact and M be a module over L. In this paper we generalize the concepts of an element prime to another element and an element primary to another element in a lattice module M and obtain the characterizations of an element prime to another element and an element primary to another element in a lattice module.