Turkish Journal of Mathematics
Abstract
Let $R$ be a finite commutative principal ideal ring with unity. In this article, we prove that the zero-divisor graph $\Gamma(R)$ is a divisor graph if and only if $R$ is a local ring or it is a product of two local rings with at least one of them having diameter less than $2$. We also prove that $\Gamma(R)$ is a divisor graph if and only if $\Gamma(R[x])$ is a divisor graph if and only if $\Gamma(R[[x]])$ is a divisor graph.
DOI
10.3906/mat-1601-102
Keywords
Principal ideal ring, zero-divisor graph, divisor graph, polynomial ring, power series ring
First Page
797
Last Page
807
Recommended Citation
OSBA, E. A, & ALKAM, O (2017). When zero-divisor graphs are divisor graphs. Turkish Journal of Mathematics 41 (4): 797-807. https://doi.org/10.3906/mat-1601-102
