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Skew Derivations with Central Invariants

Authors:	Bergen Jeffrey; Grzeszczuk Piotr

Institution:	Department of Mathematics, DePaul University Chicago, IL 60614 USA. E-mail: jbergen{at}condor.depaul.edu Institute of Mathematics, University of Bia $l$ ystok 15-267, Bia $l$ ystok, Poland. E-mail: piotrgr{at}cksr.ac.bialystok.pl

Abstract:	If ${sigma}$ is an automorphism and ${delta}$ is a ${sigma}$ -derivation of a ring R, thenthe subring of invariants is the set R⁽⁾={r $isin$ R\| ${delta}$ (r)=0}. The mainresult of this paper is ‘let R be a semiprime ring withan algebraic ${sigma}$ -derivation ${delta}$ such that R⁽⁾ is central; then R iscommutative’. This theorem generalizes results on theinvariants of automorphisms and derivations and is proved byreducing down to the special cases of automorphisms and derivations.

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