*-alpha-derivation on prime *-rings

Let \Re be an associative ring with involution *. An additive map \lambda\rightarrow \lambda^{*} of \Re into itself is called an involution if the following conditions are satisfied (i) (\lambda\mu)^{*}=\mu^{*}\lambda^{*}, (ii) (\lambda^{*})^{*}=\lambda ~~ \mbox{for all}~ \lambda,\mu\in \Re. A ring equipped with an involution is called an *-ring or ring with involution. The aim of the present paper is to establish some results on *-\alpha-derivations in *-rings and investigate the commutativity of prime *-rings admitting *-\alpha-derivations on \Re satisfying certain identities also prove that if \Re admits a reverse *-\alpha-derivation \delta of \Re, then \alpha\in Z(\Re) and some related results have also been discussed.

کلیدواژه ها:

Prime *-ring ، *- α- derivation ، reverse *- α-derivation