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Embedding rational division algebras


Author: Burton Fein
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
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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 [Enhancements On Off] (What's this?)

  • [1] A. A. Albert, Structure of algebras, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R.I., 1939. MR 1, 99. MR 0123587 (23:A912)
  • [2] E. Artin and J. Tate, Class field theory, Harvard Univ. Press, Cambridge, Mass., 1961. (Cf. MR 36 #6383.)
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  • [4] B. Fein and M. Schacher, Embedding finite groups in rational division algebras. I, J. Algebra 17 (1971), 412-428. MR 0272821 (42:7702)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289568-9
Keywords: Rational division algebra, Hasse invariant, Grünwald-Wang theorem
Article copyright: © Copyright 1972 American Mathematical Society

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