A simple proof of a theorem of Albert
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- by M. L. Racine PDF
- Proc. Amer. Math. Soc. 43 (1974), 487-488 Request permission
Abstract:
A simple proof is given of the following theorem of Albert: An associative division algebra of degree 4 over its center is of order 4 in the Brauer group if and only if it cannot be written as a tensor product of quaternion algebras.References
- A. Adrian Albert, New results in the theory of normal division algebras, Trans. Amer. Math. Soc. 32 (1930), no. 2, 171–195. MR 1501532, DOI 10.1090/S0002-9947-1930-1501532-5
- A. Adrian Albert, Normal division algebras of degree four over an algebraic field, Trans. Amer. Math. Soc. 34 (1932), no. 2, 363–372. MR 1501642, DOI 10.1090/S0002-9947-1932-1501642-4 —, Structure of algebras, Amer. Math. Soc. Colloq. Publ., vol. 24, Amer. Math. Soc., Providence, R.I., 1939. MR 1, 99.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 487-488
- MSC: Primary 16A40
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330218-2
- MathSciNet review: 0330218