A NOTE ON SEMIDERIVATIONS
Journal Title: Bulletin of Pure and Applied Sciences Sec. E - Mathematics and Statistics - Year 2018, Vol 37, Issue 2
Abstract
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∈R, then F is called a generalized semiderivation of R. We prove that every generalized semiderivation of a prime ring R is either an ordinary generalized derivation of R or a semiderivation of R.
Authors and Affiliations
Gurninder S. Sandhu
Keywords
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