Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T04:45:01.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Centralizing Automorphisms of Lie Ideals in Prime Rings

Published online by Cambridge University Press:  20 November 2018

Joseph H. Mayne
Joseph H. Mayne*
Affiliation:
Department of Mathematical Sciences Loyola University of Chicago Chicago, Illinois 60626 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a prime ring of characteristic not equal to two and let T be an automorphism of R. If U is a Lie ideal of R such that T is nontrivial on U and xxT — xTx is in the center of R for every x in U, then U is contained in the center of R.

Keywords

16A6816A7016A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 510 - 514
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Awtar, R., Lie and Jordan structures in prime rings with derivations, Proc. Amer. Math. Soc. 41(1973), 67–74.Google Scholar
2. Bell, H. E. and Martindale, W. S., III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30(1987), 92–101.Google Scholar
3. Bergen, J., Herstein, I. N. and Kerr, J. W., Lie ideals and derivations of prime rings, J. Algebra 71(1981), 259–267.Google Scholar
4. Lee, P. H. and Lee, T. K., Lie ideals of prime rings with derivations, Bull. Inst. Math. Acad. Sinica. 11(1983), 75–80.Google Scholar
5. Mayne, J., Centralizing automorphisms of prime rings, Canad. Math. Bull. 19(1976), 113–115.Google Scholar
6. Mayne, J., Centralizing mappings of prime rings, Canad. Math. Bull. 27(1984), 122–126.Google Scholar
7. Posner, E., Derivations in prime rings, Proc. Amer. Math. Soc. 8(1957), 1093–1100.Google Scholar
8. Smiley, M. F., Remarks on the commutativity of rings, Proc. Amer. Math. Soc. 10(1959), 466–470.Google Scholar