∗-α-DERIVATION ON PRIME ∗-RINGS

Let R be an associative ring with involution ∗. An additive map λ → λ* of R into itself is called an involution if the following conditions are satisfied (i)(λµ)* = µ*λ* , (ii)(λ*)* = λ for all λ, µ ∈ R . 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 ∗-α-derivation in ∗-rings and investigate the commutativity of prime ∗-rings admitting ∗-α-derivation on R satisfying certain identities also prove that if R admits a reverse ∗-α-derivation δ of R, then α ∈ Z(R) and some related results have also been discussed.