Strong skew commutativity preserving maps on rings. (Q2788671)

Let \(A\) be a unital ring with involution. The paper is concerned with a (not necessarily additive) map \(\varphi\colon A\to A\) that satisfies \(\varphi(a)\varphi(b)-\varphi(b)\varphi(a)^*=ab-ba^*\) for all \(a,b\in A\). Under certain technical conditions, which are in particular fulfilled if \(A\) is a prime ring containing a nontrivial symmetric idempotent, it is shown that \(\varphi\) is of the form \(\varphi(a)=za+f(a)\) where \(z\) and \(f(a)\) are symmetric central elements.