In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article

Author

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran

Abstract

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 $.

Keywords