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Paper   IPM / M / 8955
School of Mathematics
  Title:   Zero divisor graphs for modules over commutative rings
  Author(s):  M. Behboodi
  Status:   Published
  Journal: J. Commut. Algebra
  Vol.:  4
  Year:  2012
  Pages:   175-198
  Supported by:  IPM
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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