On Ideals and Commutativity of Prime Rings with Generalized Derivations
Keywords:Left ideals, prime rings, centralizing, derivations, generalized derivations, commutativity.
AbstractAn additive mapping F: R â†’ R is called a generalized derivation on R if there exists a derivation d: R â†’ R such that F(xy) = xF(y) + d(x)y holds for all x,y âˆˆ R. It is called a generalized (Î±,Î²)âˆ’derivation on R if there exists an (Î±,Î²)âˆ’derivation d: R â†’ R such that the equation F(xy) = F(x)Î±(y)+Î²(x)d(y) holds for all x,y âˆˆ R. In the present paper, we investigate commutativity of a prime ring R, which satisï¬es certain diï¬€erential identities on left ideals of R. Moreover some results on commutativity of rings with involutions that satisfy certain identities are proved.
How to Cite
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.