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Centralizing Mappings of 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
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Abstract

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Let R be a prime ring and U be a nonzero ideal or quadratic Jordan ideal of R. If L is a nontrivial automorphism or derivation of R such thatuL(u)—L(u)u is in the center of R for every u in U, then the ring R is commutative.

Keywords

16A1216A6816A7016A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 122 - 126
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Awtar, R., Lie and Jordan structures in prime rings with derivations, Proc. Amer. Math. Soc, 41 (1973), 67-74.Google Scholar
2. Mayne, J., Centralizing automorphisms of prime rings, Canad, Math. Bull., 19(1) (1976), 113-115.Google Scholar
3. Mayne, J., Ideals and centralizing mappings in prime rings, Proc. Amer. Math. Soc, 86 (1982), 211-212. Erratum 89 (1983), 187.Google Scholar
4. McCrimmon, K., On Herstein's theorems relating Jordan and associative algebras, J. Algebra, 13 (1969), 382-392.Google Scholar
5. Posner, E., Derivations in prime rings, Proc. Amer. Math. Soc, 8 (1957), 1093-1100.Google Scholar