A Note on Semiderivations

Abstract

Recently, Filippis et al. introduced the notion of generalized semiderivation [[5], Definition 1.2] in prime rings. Accordingly, let  be a prime ring and  be an additive mapping. If there exists a semiderivation  associated with an endomorphism  of  such that  and  for all , then  is called a generalized semiderivation of . We prove that every generalized semiderivation of a prime ring  is either an ordinary generalized derivation of  or a semiderivation of.