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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On prime nonprimitive von Neumann regular algebras


Authors: Gene Abrams, Jason P. Bell and Kulumani M. Rangaswamy
Journal: Trans. Amer. Math. Soc. 366 (2014), 2375-2392
MSC (2010): Primary 16G20, 05E10
Published electronically: January 17, 2014
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Abstract: Let $ E$ be any directed graph, and $ K$ any field. We classify those graphs $ E$ for which the Leavitt path algebra $ L_K(E)$ is primitive. As a consequence, we obtain classes of examples of von Neumann regular prime rings which are not primitive.


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Additional Information

Gene Abrams
Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80918
Email: abrams@math.uccs.edu

Jason P. Bell
Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A1S6
Address at time of publication: Department of Pure Mathematics, University of Waterloo, 200 University Avenue W, Waterloo, Ontario, Canada N2L 3G1
Email: jpb@sfu.ca, jpbell@uwaterloo.ca

Kulumani M. Rangaswamy
Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80918
Email: krangasw@uccs.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05878-9
PII: S 0002-9947(2014)05878-9
Keywords: Leavitt path algebra, prime ring, primitive ring, countable separation property
Received by editor(s): May 16, 2011
Received by editor(s) in revised form: April 4, 2012, and May 15, 2012
Published electronically: January 17, 2014
Additional Notes: The first author was partially supported by the U.S. National Security Agency under grant number H89230-09-1-0066.
The second author was supported by NSERC grant 31-611456.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.