Embedding rational division algebras
HTML articles powered by AMS MathViewer
- by Burton Fein PDF
- Proc. Amer. Math. Soc. 32 (1972), 427-429 Request permission
Abstract:
Necessary and sufficient conditions are given for two K-division rings, K an algebraic number field, to have precisely the same set of subfields. Using this, an example is presented of two K-division rings having precisely the same set of subfields such that only one of the division rings can be embedded in a Q-division ring.References
- A. Adrian Albert, Structure of algebras, American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. Revised printing. MR 0123587 E. Artin and J. Tate, Class field theory, Harvard Univ. Press, Cambridge, Mass., 1961. (Cf. MR 36 #6383.)
- Max Deuring, Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 41, Springer-Verlag, Berlin-New York, 1968 (German). Zweite, korrigierte auflage. MR 0228526
- Burton Fein and Murray Schacher, Embedding finite groups in rational division algebras. I, J. Algebra 17 (1971), 412–428. MR 272821, DOI 10.1016/0021-8693(71)90023-8
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 427-429
- MSC: Primary 16.46
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289568-9
- MathSciNet review: 0289568