Sayed Kahlil Ekrami
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), ...
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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 $.
