Double Ore Extensions versus Iterated Ore Extensions

Abstract

Motivated by the construction of new examples of Artin-Schelter regular algebras of global dimension four, J.J. Zhang and J. Zhang (2008) introduced an algebra extension AP[y1,y2;σ,δ,τ] of A, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over A. The aim of this paper is to describe those double Ore extensions which can be presented as iterated Ore extensions of the form A[y1;σ1, δ1][y2;σ2, δ2]. We also give partial answers to some questions posed in Zhang and Zhang (2008).