On strong commutativity preserving like maps in rings with involution

Abstract

The main purpose of this paper is to prove the following result: Let R be a prime ring with involution of the second kind and with char.R/ 6 D 2. If R admits a nonzero derivation d W R ! R such that OEd.x/; d.x / D OEx; x for all x 2 R, then R is commutative. We also provide an example which shows that the above result does not holds in case the involution is of the first kind. Moreover, a related result has also been obtained.