2018•International Electronic Journal of AlgebraOpen access

On the ideal-based zero-divisor graphs

H. Ansari-Toroghy, F. Farshadifar, Farideh Mahboobi-Abkenar

Abstract

Let R be a commutative ring. In this paper, we study the annihilator ideal-based zero-divisor graph by replacing the ideal I of R with the ideal AnnR(M) for an R-module M. Also, we investigate a certain subgraph of the annihilator ideal-based zero-divisor graph and obtain some related results.

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Key concepts: Zero divisor, Annihilator, Mathematics, Ideal (ethics), Primary ideal, Commutative ring, Zero (linguistics), Divisor (algebraic geometry)