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Centralizing Automorphisms of Prime Rings

Published online by Cambridge University Press:  20 November 2018

Joseph H. Mayne
Joseph H. Mayne*
Affiliation:
Applied Mathematics Division, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A. Department of Mathematics, Loyola University, Chicago, Illinois 60626, U.S.A.
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Abstract

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Let R be a prime ring and T be a nontrivial automorphism of R. If xxT—xTx is in the center of the ring for every x in R, then R is a commutative integral domain.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 113 - 115
Copyright
Copyright © Canadian Mathematical Society 1976

References

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3. Luh, J., “A note on commuting automorphisms of rings,” Amer. Math. Monthly 77 (1970), 61–62.Google Scholar
4. Posner, E., “Derivations in prime rings,” Proc. Amer. Math. Soc. 8 (1957), 1093–1100.Google Scholar