Associated graphs of le-modules

Abstract

Let M be an le-module over a commutative ring with unity. In this paper, an associated graph G(M) of M with all nonzero proper submodule elements of M as vertices has been introduced and studied. Any two distinct vertices n and m are adjacent if n+m = e. Some algebraic, topological and, graph theoretic properties of le-modules have been established. Also, it is shown that the Beck's conjecture is true for coatomic le-modules.