Jordan homoderivation behavior of generalized derivations in prime rings - Bera, Nripendu; Dhara, Basudeb (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 512.5Suppose that $R$ is a prime ring with ${\rm char}(R) eq 2$ 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 $h\colon R→ R$ is called homoderivation if $h(ab) = h(a)h(b)+h(a)b+ah(b)$ for all $a,b\in R.$ 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 $ξ \in f(R) = \{f(ξ_1,…,ξ_n) \mid ξ_1,…,ξ_n\in R\}.$