Pseudo-Primary, Classical Prime and Pseudo-Classical Primary Elements in Lattice Modules

Abstract

In this paper, we introduce the notion of pseudo-primary elements and pseudo-classical primary elements in an L-module M and obtain their characterizations. The aim of the paper is to show rad(N ) ∈ M , the radical of N ∈ M is prime if N is either pseudo-primary or pseudo-classical primary. Also, we study classical prime elements of an L-module M to obtain many of its characterizations and its properties.