Commuting-like elements in prime rings with derivations (Q2154680)

In this paper, the authors show that certain elements, defined by commutativity conditions involving derivations over prime rings, are either central elements or they classify the involved derivations. They also provide examples to show that the obtained results (Theorems 3.1, 3.5, 3.7, and 3.10) cannot be extended to semi-prime rings. In example 3.13 (1) they prove the results of Theorems 3.1, 3.7, and 3.10 can not be extended to semi-prime rings, and in example 3.13 (2) they prove the result of Theorems 3.5 can not be extended to semi-prime rings.