On a new extension of the zero-divisor graph

2018/06/28 by Cherrabi, A., Essannouni, H., Jabbouri, E. +1
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.11442

Abstract

In this paper, we introduce a new graph whose vertices are the nonzero zero-divisors of commutative ring R and for distincts elements x and y in the set Z(R)^⋆ of the nonzero zero-divisors of R, x and y are adjacent if and only if xy=0 or x+y∈ Z(R). we present some properties and examples of this graph and we study his relation with the zero-divisor graph and with a subgraph of total graph of a commutative ring.

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