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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Primitivity of prime countable-dimensional regular algebras
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by Pere Ara and Jason P. Bell PDF
Proc. Amer. Math. Soc. 143 (2015), 2759-2766 Request permission

Abstract:

Let $k$ be a field and let $R$ be a countable-dimensional prime von Neumann regular $k$-algebra. We show that $R$ is primitive, answering a special case of a question of Kaplansky.
References
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Additional Information
  • Pere Ara
  • Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
  • MR Author ID: 206418
  • Email: para@mat.uab.cat
  • Jason P. Bell
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Canada
  • MR Author ID: 632303
  • Email: jpbell@uwaterloo.ca
  • Received by editor(s): September 11, 2013
  • Received by editor(s) in revised form: October 15, 2013, and November 18, 2013
  • Published electronically: March 11, 2015
  • Additional Notes: The first-named author was partially supported by DGI MINECO MTM2011-28992-C02-01, by FEDER UNAB10-4E-378 “Una manera de hacer Europa”, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya
    The second-named author was supported by NSERC grant 31-611456
  • Communicated by: Birge Huisgen-Zimmermann
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 2759-2766
  • MSC (2010): Primary 16E50; Secondary 16D60, 16N60
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12434-3
  • MathSciNet review: 3336601