Lie Nilpotent Centrally Essential Rings

A ring R is said to be centrally essential if either R is commutative or for any non-central element [Formula: see text], there exist two non-zero central elements x and y with [Formula: see text]. In this paper, we study centrally essential rings which are nilpotent as Lie rings (centrally essential rings are not necessarily nilpotent as Lie rings, since it is known that they are not necessarily PI rings). It is proved that the following rings are Lie nilpotent: right Artinian centrally essential rings with finitely generated adjoint group, semiperfect centrally essential rings with torsion group of units and nilpotent Jacobson radical, the right uniserial centrally essential rings.