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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



Simultaneous embeddings of finite dimensional division algebras

Authors: Louis Rowen and David Saltman
Journal: Proc. Amer. Math. Soc. 141 (2013), 737-744
MSC (2010): Primary 16K20, 16K40, 12E15; Secondary 16K50
Published electronically: November 19, 2012
MathSciNet review: 3003667
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Abstract: L. Small asked whether two finite dimensional division algebras containing a common central subfield $ F$ are embeddable in a common division algebra. Although we have a counterexample, the question is answered affirmatively for division algebras whose centers are finitely generated over a common perfect subfield.

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Additional Information

Louis Rowen
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel

David Saltman
Affiliation: Center for Communications Research-Princeton, 805 Bunn Drive, Princeton, New Jersey 08540

Keywords: Division algebra, cyclic algebra, embedding, Schur index, index reduction, Weyl transfer, profinite group
Received by editor(s): September 13, 2010
Received by editor(s) in revised form: April 17, 2011
Published electronically: November 19, 2012
Additional Notes: This work was supported by the U.S.-Israel Binational Science Foundation (grant No. 2010149).
Communicated by: Harm Derksen
Article copyright: © Copyright 2012 Institute for Defense Analyses

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