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A GENERALIZATION OF THE ZERO-DIVISOR GRAPH FOR MODULES

A GENERALIZATION OF THE ZERO-DIVISOR GRAPH FOR MODULES

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say <TEX>${\Gamma}(M)$</TEX>, such that when M = R, <TEX>${\Gamma}(M)$</TEX> is exactly the classic zero-divisor graph. Many well-known results by D. F. Anderson and P. S. Livingston, in [5], and …