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

Abstract

This paper continues the ongoing effort to study the compressed zero-divisor graph over noncommutative 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 ?E(R[x; ?,?]), where the base ring R is reversible and also have the (?,?)-compatible property. Also, we give a complete characterization of the diameter of ?E (R[[x;?]]), where R is a reversible, ?-compatible and right Noetherian ring. By some examples, we show that all of the assumptions ?reversiblity?, ?(?,?)-compatiblity? and ?Noetherian? in our main results are crucial.