Burchnall-Chaundy theory for skew Poincar\'e-Birkhoff-Witt extensions

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 Poincar'e-Birkhoff-Witt extensions.