فهرست نشریات علمی دسترسی آزاد ایران

In this paper‎, ‎we prove that every orthogonally higher ring derivation is a higher ring derivation‎. ‎Also we find the general solution of the pexider orthogonally higher ring derivations‎‎\begin{align*}‎‎\left\{‎‎\begin{array}{lr}‎‎f_n(x+y)=g_n(x)+h_n(y)‎, ‎\;\left\langle x,y \right\rangle =0,\\‎‎f_n(xy) = \sum_{i+j=n} g_i(x)h_j(y)‎.‎\end{array}‎‎\right‎.‎\end{align*}‎‎Then we prove that for any approximate pexider orthogonally higher ring derivation under some control functions $ \varphi(x,y) $ and $ \psi(x,y) $‎, ‎there exists a unique higher ring derivation $ D=\{d_n\}_{n=0}^\infty $‎, ‎near $ \{f_n\}_{n=0}^\infty $‎, ‎$ \{g_n\}_{n=0}^\infty $ and $ \{h_n\}_{n=0}^\infty $ estimated by $ \varphi $ and $ \psi $.