Extending automorphisms and derivations onto Ore-extensions (Q889138)

The authors study the extendability of an automorphism \(\sigma\) of a field \(K\) to an automorphism \(\tau\) of the classical right ring of quotients \(Q= K(x;\alpha,\delta)\) of the Ore-extension \(R= K[x;\alpha,\delta]\) and extendability of \(\sigma\)-derivation \(\varepsilon\) of \(K\) to a \(\tau\)-derivation of \(\sigma\). They provide a criterion for extendability of \(\sigma\). Also they characterize all extensions of automorphisms \(\sigma\) from \(K\) to \(Q\). Under some additional assumptions, the authors obtain a characterization of the extensions of \(\sigma\)-derivations \(\varepsilon\).