A GENERALIZATION OF THE ZERO-DIVISOR GRAPH FOR MODULES

@article{Safaeeyan2014AGO,
  title={A GENERALIZATION OF THE ZERO-DIVISOR GRAPH FOR MODULES},
  author={Saeed Safaeeyan and Mohammad Reza Baziar and Ehsan Momtahan},
  journal={Journal of Korean Medical Science},
  year={2014},
  volume={51},
  pages={87-98}
}
Abstract. Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say Γ(M), such thatwhen M = R, Γ(M) is exactly the classic zero-divisor graph. Many well-known results by D. F. Anderson and P. S. Livingston, in [5], and by D. F.Anderson and S. B. Mulay, in [6], have been generalized for Γ(M) in thepresent article. We show that Γ(M) is connected with diam(Γ(M)) ≤ 3.We also show that for a reduced module M with Z(M) ∗ 6= M \ {0},gr(Γ(M)) = ∞ if and… 

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