Simultaneous embeddings of finite dimensional division algebras
HTML articles powered by AMS MathViewer
- by Louis Rowen and David Saltman PDF
- Proc. Amer. Math. Soc. 141 (2013), 737-744
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.References
- P. M. Cohn, The embedding of firs in skew fields, Proc. London Math. Soc. (3) 23 (1971), 193–213. MR 297814, DOI 10.1112/plms/s3-23.2.193
- Burton Fein, David J. Saltman, and Murray Schacher, Embedding problems for finite-dimensional division algebras, J. Algebra 167 (1994), no. 3, 588–626. MR 1287062, DOI 10.1006/jabr.1994.1204
- Nathan Jacobson, Basic algebra. II, W. H. Freeman and Co., San Francisco, Calif., 1980. MR 571884
- Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
- Serge Lang, Algebraic number theory, 2nd ed., Graduate Texts in Mathematics, vol. 110, Springer-Verlag, New York, 1994. MR 1282723, DOI 10.1007/978-1-4612-0853-2
- David J. Saltman, The Schur index and Moody’s theorem, $K$-Theory 7 (1993), no. 4, 309–332. MR 1246280, DOI 10.1007/BF00962052
Additional Information
- Louis Rowen
- Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
- MR Author ID: 151270
- Email: rowen@macs.biu.ac.il
- David Saltman
- Affiliation: Center for Communications Research-Princeton, 805 Bunn Drive, Princeton, New Jersey 08540
- MR Author ID: 153620
- Email: saltman@idaccr.org
- 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
- © Copyright 2012 Institute for Defense Analyses
- Journal: Proc. Amer. Math. Soc. 141 (2013), 737-744
- MSC (2010): Primary 16K20, 16K40, 12E15; Secondary 16K50
- DOI: https://doi.org/10.1090/S0002-9939-2012-11269-9
- MathSciNet review: 3003667