Let be a -torsion free -prime ring, a derivation which commutes with and a -Jordan ideal and a subring of . In this paper, it is shown that if either acts as a homomorphism or as an anti-homomorphism on , then or . Furthermore, an example is given to demonstrate that the -primeness hypothesis is not superfluous.
In this paper we investigate -prime near-rings with derivations satisfying certain differential identities on Jordan ideals, and we provide examples to show that the assumed restrictions cannot be relaxed.
Let be a prime ring and a nonzero ideal of The purpose of this paper is to classify generalized derivations of satisfying some algebraic identities with power values on More precisely, we consider two generalized derivations and of satisfying one of the following identities:
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