Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T10:46:21.933Z Has data issue: false hasContentIssue false
  • English
  • Français

Semisimplicity of Free Centred Extensions

Published online by Cambridge University Press:  20 November 2018

Miguel Ferrero
Miguel Ferrero*
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900 Porto Alegre Brazil, e-mail:Ferrero@ifI.ufrgs.br
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.

We prove that a free centred extension R[E] is a semisimple ring if R is a semisimple ring and C[E] is semisimple for every field C which is the extended centroid of a primitive factor of R.

Keywords

16S2016D60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 55 - 58
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Ferrero, M., Closed and prime ideals in free centred extensions, J. Algebra 148(1992), 1–16.Google Scholar
2. Ferrero, M., Centred bimodules over prime rings: closed submodules and applications to ring extensions, J. Algebra, to appear.Google Scholar
3. Ferrero, M. and Parmenter, M. M., A note on Jacobson rings and polynomial rings, Proc. Amer. Math. Soc. 104(1988), 281–286.Google Scholar
4. Krempa, J., On semisimplicity of tensor products, Lecture Notes in Pure and Appl. Math. 51, Dekker, New York, 1979, 105–122,Google Scholar
5. Passman, D. S., The algebraic structure of group rings, John Wiley, New York, 1977.Google Scholar
6. Stenström, B., Rings of quotients, Springer-Verlag, Berlin, Heidelberg, New York, 1975.Google Scholar