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Derivations in Prime Rings

Published online by Cambridge University Press:  20 November 2018

Jeffrey Bergen
Jeffrey Bergen*
Affiliation:
University of Chicago Chicago, Illinois 60637
*
Current Address: DePaul University Chicago, Illinois 60614.
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Abstract

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Let R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.

Keywords

16A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 267 - 270
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Herstein, I. N., A note on derivations, Canadian Math. Bull. 21 (1978), 369-370.Google Scholar
2. Kovacs, Amos, On derivations in prime rings and a question of Herstein, Canadian Math. Bull. 22 (1979), 339-344.Google Scholar