On the diameter of compressed zero-divisor graphs of Ore extensions

Ebrahim Hashemi, Mona Abdi


This paper continues the ongoing effort to study the compressed zero-divisor graph over non-commutative rings.
The purpose of our paper is to study
the diameter of the  compressed zero-divisor graph of Ore extensions and give a complete characterization of the possible diameters of $\Gamma_{E} \big(R[x; \alpha, \delta]\big)$, where the base ring $R$ is reversible and also have the $(\alpha , \delta)$-compatible property. Also, we give a complete characterization of the diameter of $\Gamma_{E}\big( R[[x; \alpha]]\big) $, where $R$ is a  reversible, $\alpha$-compatible and right Noetherian ring.  By some examples, we show that all of the assumptions ``reversiblity'',  ``$(\alpha,\delta)$-compatiblity" and  ``Noetherian" in our main results  are crucial.


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