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
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