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Journal of the London Mathematical Society 1999 59(1):87-99; doi:10.1112/S0024610799007000
© 1999 by London Mathematical Society
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© The London Mathematical Society

Skew Derivations with Central Invariants

Jeffrey Bergen and Piotr Grzeszczuk

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

Received 3 December 1995. Revision received 30 June 1996.

If {sigma} is an automorphism and {delta} is a {sigma}-derivation of a ring R, then the subring of invariants is the set R({delta})={risinR|{delta}(r)=0}. The main result of this paper is ‘let R be a semiprime ring with an algebraic {sigma}-derivation {delta} such that R({delta}) is central; then R is commutative’. This theorem generalizes results on the invariants of automorphisms and derivations and is proved by reducing down to the special cases of automorphisms and derivations.


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