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| Paper IPM / M / 8955 |
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| Abstract: | |
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In this article, we give several generalizations of the concept of zero-divisor elements
in a commutative ring with identity to modules. Then for each R-module
M we associate three undirected (simple) graphs Γ*(RM) ⊆ Γ(RM) ⊆ Γ*(RM)
which, for M=R all coincide with the zero-divisor graph of R. The main object
of this paper is to study the interplay of module-theoretic properties of M with
graph-theoretic properties of these graphs.
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