Abstract
Herstein proved that a prime ring R of is commutative if there is a nonzero derivation d of R such that for all The aim of this paper is to prove the -version of Herstein’s result with a pair of derivations on prime ideals of a ring with involution. Precisely, we prove the following result: let R be a ring with involution of the second kind, P a prime ideal of R such that and If d 1 and d 2 are derivations of R satisfying the condition for all then one of the following holds: (a) (b) (c) R/P is a commutative integral domain. Moreover, some related results are also discussed. As consequences of our main theorems, many known results can be either generalized or deduced.
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