### Automorphisms and derivations on the center of a ring

*V. K. Bhat*

#### Abstract

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 $S\subseteq Z(O_{1}(R))$,

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.

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.

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