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Strong Commutativity Preserving Maps of Semiprime Rings

Published online by Cambridge University Press:  20 November 2018

Matej Brešar  and
C. Robert Miers
Matej Brešar
Affiliation:
University of Maribor, PF Koroska 160 62000 Maribor Slovenia
C. Robert Miers
Affiliation:
Department of Mathematics and Statistics, P.O. Box 3045 University of Victoria Victoria, British Columbia V8W 3P4
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Abstract

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In this paper we characterize maps f: R —> R where R is semiprime, f is additive, and [f(x),f(y)] = [x,y] for all x,y ∊ R. It is shown that f(x) = λx + ξ(x) where λ ∊ C, λ2 = 1, and ξ: R —> C is additive where C is the extended centroid of R.

Keywords

16N60semiprime ringextended centroidstrong commutativity preserving
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 457 - 460
Copyright
Copyright © Canadian Mathematical Society 1994

References

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