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Centralizing Mappings of Semiprime Rings

Published online by Cambridge University Press:  20 November 2018

H. E. Bell  and
W. S. Martindale III
H. E. Bell
Affiliation:
Department of Mathematics Brock University St. Catharines, Ontario Canada L2S 3A1
W. S. Martindale III
Affiliation:
Department of Mathematics and Statistics University of Massachusetts Amherst, Massachusetts 01003
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Abstract

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Let R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.

Keywords

16A7216A70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 92 - 101
Copyright
Copyright © Canadian Mathematical Society 01

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