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SKEW DERIVATIONS WITH CENTRAL INVARIANTS

Published online by Cambridge University Press:  01 February 1999

JEFFREY BERGEN  and
PIOTR GRZESZCZUK
JEFFREY BERGEN
Affiliation:
Department of Mathematics, DePaul University, Chicago, IL 60614 USA. E-mail: [email protected]
PIOTR GRZESZCZUK
Affiliation:
Institute of Mathematics, University of Białystok, 15-267, Białystok, Poland. E-mail: [email protected]
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Abstract

If σ is an automorphism and δ is a σ-derivation of a ring R, then the subring of invariants is the set R(δ)={r∈R[mid ]δ(r)=0}. The main result of this paper is ‘let R be a semiprime ring with an algebraic σ-derivation δ such that R(δ) 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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 87 - 99
Copyright
The London Mathematical Society 1999

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