Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T13:15:36.582Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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.

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

1. Ara, P. and Mathieu, M., An application of local multipliers to centralizing mappings of C*-algebras, Quart. J. Math., Oxford 44(1993), 129–138.Google Scholar
2. Bell, H. and Daif, M., On commutativity and strong commutativity preserving maps, preprint.Google Scholar
3. Bell, H. and Mason, G., On derivations in near rings and rings, Math. J. Okagama Univ., 37(1994), 443–447.Google Scholar
4. Bresar, M., On certain pairs of functions of semiprime rings, Proc. Amer. Math. Soc. 129(1994), 709–713.Google Scholar