Action of higher derivations on prime rings with involution

In this paper, we monitor the behavior of a prime ring with involution of second kind. Such rings are studied through the prism of higher derivations satisfying certain differential identities. Precisely, we prove that for a higher derivation D = ( d i ) i is an element of N boolean OR { 0 }, if we are able to establish the identity, d n [ x , x * ] is an element of Z ( R ) for a single positive integer n, then the structure exhibits certain interesting properties. Some similar looking results are also presented.