Jordan homoderivation behavior of generalized derivations in prime rings - Bera, Nripendu; Dhara, Basudeb (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 512.5 Suppose that R is a prime ring with char(R) eq 2 and f(ξ_1,…,ξ_n) is a noncentral multilinear polynomial over C( = Z(U)), where U is the Utumi quotient ring of R. An additive mapping hR→ R is called homoderivation if h(ab) = h(a)h(b)+h(a)b+ah(b) for all a,bR. We investigate the behavior of three generalized derivations F, G, and H of R satisfying the condition F(ξ^2) = G(ξ)^2+H(ξ)ξ+ξ H(ξ) for all ξ f(R) = {f(ξ_1,…,ξ_n) ξ_1,…,ξ_nR}.