1Department of Mathematics, Multani Mal Modi College, Patiala, Punjab-147001, India
Department of Mathematics, Punjabi University, Patiala, Punjab-147002
*Corresponding Author: Gurninder S. Sandhu, Department of Mathematics, Punjabi University, Patiala, Punjab-147002; Department of Mathematics, Multani Mal Modi College, Patiala, Punjab-147001, India. E-mail: gurninder_rs@pbi.ac.in
Online published on 18 December, 2018.
Recently, Filippis et al. introduced the notion of generalized semiderivation [[5], Definition 1.2] in prime rings. Accordingly, let R be a prime ring and F: R → R be an additive mapping. If there exists a semiderivation d associated with an endomorphism g of R such that F(xy) = F(x)g(y) + xd(y) = F(x)y + g(x)d(y) and F(g(x)) = g(F(x)) for all x, y ε R, then F is called a generalized semiderivation of F. We prove that every generalized semiderivation of a prime ring R is either an ordinary generalized derivation of R or a semiderivation of R
Prime ring, Semiprime ring, Semiderivation, Multiplicative semiderivation
