On the diameter of the zero-divisor graph over skew PBW extensions

Abstract

The aim of this paper is to investigate the interplay between the algebraic properties of a skew Poincaré–Birkhoff–Witt extesion ring [Formula: see text] and the graph-theoretic properties of its zero-divisor graph. We are interested in studying the diameter of the zero-divisor graph of skew PBW extension rings. Among other results, we give a complete characterization of the possible diameters of [Formula: see text] in terms of the diameter of [Formula: see text].