# On the Zero-Divisor Graph of a Ring

```@article{Anderson2008OnTZ,
title={On the Zero-Divisor Graph of a Ring},
author={David F. Anderson and Ayman Badawi},
journal={Communications in Algebra},
year={2008},
volume={36},
pages={3073 - 3092}
}```
• Published 13 August 2008
• Mathematics
• Communications in Algebra
Let R be a commutative ring with identity, Z(R) its set of zero-divisors, and Nil(R) its ideal of nilpotent elements. The zero-divisor graph of R is Γ(R) = Z(R)\{0}, with distinct vertices x and y adjacent if and only if xy = 0. In this article, we study Γ(R) for rings R with nonzero zero-divisors which satisfy certain divisibility conditions between elements of R or comparability conditions between ideals or prime ideals of R. These rings include chained rings, rings R whose prime ideals…
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