Simultaneous embeddings of finite dimensional division algebras

Rowen, Louis; Saltman, David

doi:10.1090/S0002-9939-2012-11269-9

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