Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T10:50:52.141Z Has data issue: false hasContentIssue false
  • English
  • Français

On Commutativity and Strong Commutativity-Preserving Maps

Published online by Cambridge University Press:  20 November 2018

Howard E. Bell  and
Mohamad Nagy Daif
Howard E. Bell
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, L2S 3A1
Mohamad Nagy Daif
Affiliation:
Department of Mathematics, Faculty of Education, Umm Al-Qura University, Taif Saudi Arabia
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.

If R is a ring and S ⊆ R, a mapping f:R —> R is called strong commutativity- preserving (scp) on S if [x, y] = [f(x),f(y)] for all x,y € S. We investigate commutativity in prime and semiprime rings admitting a derivation or an endomorphism which is scp on a nonzero right ideal.

Keywords

16W2016W2516U8016N60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 443 - 447
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Bell, H. E. and Martindale, W. S., Centralizing mappings of semiprime rings, Canad. Math. Bull. 30(1987), 92–101.Google Scholar
2. Bell, H. E. and Mason, G., On derivations in near-rings and rings, Math. J. Okayama Univ. 34(1992), 135–144.Google Scholar
3. Bresar, M., Commuting traces of biadditive mappings, commutativity'-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335(1993), 525–546.Google Scholar
4. Daif, M. N. and Bell, H. E., Remarks on derivations on semiprime rings, Internat. J. Math. Math. Sci. 15(1992), 205–206.Google Scholar
5. Martindale, W. S., Prime rings satisfying a generalized polynomial identity, J. Algebra 12(1969), 576–584.Google Scholar