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Associated graphs of le-modules

Sadashiv Ramkrushna Puranik, Sachin Ballal, Vilas Kharat


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.

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