Noetherian properties of skew polynomial rings with binomial relations

Abstract

In this work we study standard finitely presented associative algebras over a fixed field K. A restricted class of skew polynomial rings with quadratic relations considered in an earlier work of M. Artin and W. Schelter will be studied. We call them binomial skew polynomial algebras. We establish necessary and sufficient conditions for such an algebra to be a Noetherian domain.