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Primitivity of prime countable-dimensional regular algebras


Authors: Pere Ara and Jason P. Bell
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
Published electronically: March 11, 2015
MathSciNet review: 3336601
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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.


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Additional Information

Pere Ara
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Email: para@mat.uab.cat

Jason P. Bell
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Canada
Email: jpbell@uwaterloo.ca

DOI: https://doi.org/10.1090/S0002-9939-2015-12434-3
Keywords: von Neumann regular rings, primitive rings, prime rings, idempotents, extended centroid, multiplier rings.
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
Article copyright: © Copyright 2015 American Mathematical Society