%0 Journal Article
%T Automorphisms and derivations on the center of a ring
%A V. K. Bhat
%J Albanian Journal of Mathematics
%D 2009
%I AulonaPress
%X Let R be a ring, $sigma_{1}$ an automorphism of R and $delta_{1}$ a $sigma_{1}$-derivation of R. Let $sigma_{2}$ be an automorphism of $O_{1}(R) = R[x; sigma_{1}, delta_{1}]$, and $delta_{2}$ be a $sigma_{2}$-derivation of $O_{1}(R)$. Let $Ssubseteq Z(O_{1}(R))$,the center of $O_{1}(R)$. Then it is proved that $sigma_{i}$ is identity when restricted to $S$, and $delta_{i}$ is zero when restricted to $S$; $i = 1, 2$. The result is proved for iterated extensions also.
%K Center
%K automorphism
%K $sigma$-derivation
%K ore extension.
%U http://journals.aulonapress.com/index.php/ajm/article/view/92/110