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In this paper we review some classical results on the algebraic dependence ofcommuting elements in several noncommutative algebras as differential operatorrings and Ore extensions. Then we extend all these results to a more generalsetting, the family of noncommutative rings known as skewPoincar\'e-Birkhoff-Witt extensions.

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