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 $A_P[y_1,y_2;\sigma ,\delta ,\tau ]$ 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 $A[y_1;{\sigma }_1,{\delta }_1][y_2;{\sigma }_2,{\delta }_2]$. We also give partial answers to some questions posed in Zhang and Zhang (2008).