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23 - M. Behboodi, Zero divisor graphs of modules over a commutative rings, Journal of Commutative Algebra, 4 (2) (2012), 175-197. (ISI)


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.

July, 2012


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