caa a22 4500 606200916 CHVBK 20210128100945.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00025-015-0447-1 doi (NATIONALLICENCE)springer-10.1007/s00025-015-0447-1 Extending Automorphisms and Derivations onto Ore-Extensions [Elektronische Daten] [Christian Karpfinger, Henning Koehler, Heinz Wähling] We study the question wether an automorphism σ of a field K can be extended to an automorphism τ of the field of fractions $${Q=K(x; \alpha, \delta)}$$ Q = K ( x ; α , δ ) of the Ore-extension $${R=K[x; \alpha, \delta]}$$ R = K [ x ; α , δ ] (Sect. 3) and wether a σ-derivation $${\varepsilon}$$ ε of K can be extended to a τ-derivation of Q (Sect. 4), and determine all extensions of σ and $${\varepsilon}$$ ε . Until now these question have only been discussed under special assumptions (for example in [7] and [11]). In particular, little is known on extensions of derivations. The result is in each case a criterion for extendability (Lemmata 3.2 and 4.3). The characterization of all extensions of automorphisms σ from K to Q is well understood (Corollary 3.5 and Theorem 3.12). This is in contrast to the characterization of the extensions of σ-derivations $${\varepsilon}$$ ε , which can only be described satisfactorily under additional assumptions (Theorems 4.8, 4.9, 4.10). We obtain the set of all extensions of σ or $${\varepsilon}$$ ε easily from a particular extension and the normalizer $${N(\sigma^{-1} \alpha \, \sigma)}$$ N ( σ - 1 α σ ) or $${N(\alpha \, \sigma)}$$ N ( α σ ) (Corollaries 3.3 and 4.4). These normalizers will be described in Sect. 2 by minimal elements of R. Springer Basel, 2015 Ore-extension nationallicence Skew polynomial ring nationallicence Skew field nationallicence Derivation nationallicence Karpfinger Christian Technische Universität München, Boltzmannstr. 3, 85747, Garching bei München, Germany aut Koehler Henning Department of Computer Science and Information Technology, Massey University, Palmerston North, New Zealand aut Wähling Heinz Technische Universität München, Boltzmannstr. 3, 85747, Garching bei München, Germany aut Results in Mathematics Springer Basel 68/3-4(2015-11-01), 395-413 1422-6383 68:3-4<395 2015 68 25 https://doi.org/10.1007/s00025-015-0447-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-015-0447-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Karpfinger Christian Technische Universität München, Boltzmannstr. 3, 85747, Garching bei München, Germany aut NATIONALLICENCE 700 1- Koehler Henning Department of Computer Science and Information Technology, Massey University, Palmerston North, New Zealand aut NATIONALLICENCE 700 1- Wähling Heinz Technische Universität München, Boltzmannstr. 3, 85747, Garching bei München, Germany aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/3-4(2015-11-01), 395-413 1422-6383 68:3-4<395 2015 68 25