Burchnall-Chaundy theory for skew Poincaré-Birkhoff-Witt extensions

Abstract

In this paper we review some classical results on the algebraic dependence of commuting elements in several noncommutative algebras as differential operator rings and Ore extensions. Then we extend all these results to a more general setting, the family of noncommutative rings known as skew Poincaré-Birkhoff-Witt extensions.

10 pages, Far East J. Math. Sci. (FJMS) (2018). arXiv admin note: text overlap with arXiv:1309.4415 by other authors