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Automorphisms and derivations on the center of a ring

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Author(s): V. K. Bhat

Journal: Albanian Journal of Mathematics
ISSN 1930-1235

Volume: 3;
Issue: 2;
Start page: 57;
Date: 2009;
Original page

Keywords: Center | automorphism | $sigma$-derivation | ore extension.

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 $Ssubseteq Z(O_{1}(R))$,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.
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