Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings

Abstract EN

Let R be a commutative ring and I an ideal of R.

The zero-divisor graph of R with respect to I, denoted ΓI(R), is the undirected graph whose vertex set is {x∈R∖I|xy∈I for some y∈R∖I} with two distinct vertices x and y joined by an edge when xy∈I.

In this paper, we extend the definition of the ideal-based zero-divisor graph to noncommutative rings.