A note on generalized left ($theta,phi$)-derivations in prime rings

Abstract

In this paper we describe generalized left ($theta, phi$)derivations in prime rings, and prove that an additive mapping in a ring R acting as a homomorphism or anti-homomorphism on an additive subgroup S of R must be either a mapping acting as a homomorphism on S or a mapping acting as an anti-homomorphism on S, through which some related results are improved.