MMN-1297
On strong commutativity preserving like maps in rings with involution
Shakir Ali; Nadeem Dar; Abdul Nadim Khan;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 such that $char(R)\not=2$. If $R$ admits a nonzero derivation $d:R\rightarrow R$ such that $[d(x),d(x^*)]=[x,x^*]$ for all $x\in R$, 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.
Vol. 16 (2015), No. 1, pp. 17-24