Generalized differential identities on prime rings and algebras

Abstract

<abstract><p>The goal of this study is to bring out the following conclusion. Let $ R $ be a noncommutative prime ring with $ 2(m+n)! $ torsion freeness and let $ m $ and $ n $ be fixed, non-negative integers and $ d, g $ be Jordan derivations on $ R $. If $ x^{m+n}d(x)+x^mg(x)x^n\in Z(R) $ or $ d(x)x^{m+n}+x^mg(x)x^n\in Z(R) $ or $ x^{n}d(x)x^{m}+x^mg(x)x^n\in Z(R) $ then $ d = g = 0 $ follows for every $ x\in R $.</p></abstract>