ON STRONG COMMUTATIVITY PRESERVING LIKE MAPS IN RINGS WITH INVOLUTION

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) not equal 2. If R admits a nonzero derivation d : R --> R such that [d(x), d(x*)] = [x, x*] for all x is an element of 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.