Geodesic
Normed Right Alternative Algebras Over the Reals
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1183-1186

Voir la notice de l'article provenant de la source Cambridge University Press

One of the most interesting results on real normed division algebras says that every real normed associative division algebra is finite dimensional [6, Theorem 1.7.6], and hence by a classical theorem of Frobenius either isomorphic to the real field, the complex field, or the algebra of quaternions. Thus the dimension of the algebra can only be either 1, 2 or 4. 
Nieto, José I. Normed Right Alternative Algebras Over the Reals. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1183-1186. doi: 10.4153/CJM-1972-127-9
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[1] 1. Albert, A. A., Absolute-valued algebraic algebras, Bull. Amer. Math. Soc. 55 (1949), 763–768. Google Scholar

[2] 2. Bruck, R. H. and Kleinfeld, E., The structure of alternative division rings, Proc. Amer. Math. Soc. 2 (1951), 878–890. Google Scholar

[3] 3. Kleinfeld, E., A characterization of the Cayley numbers, MAA Studies in Mathematics, Vol. 2: Studies in Modern Algebra. Albert, A. A., editor. Google Scholar

[4] 4. Kleinfeld, E., Right alternative rings, Proc. Amer. Math. Soc. 4 (1953), 939–944. Google Scholar

[5] 5. Milnor, J., On the parallelizability of the spheres, Bull. Amer. Math. Soc. 64 (1958), 87–89. Google Scholar

[6] 6. Rickart, C. E., Banach algebras (Van Nostrand, Princeton, 1960). Google Scholar

[7] 7. Skorniakov, L. A., Right alternative division rings (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 177–184. Google Scholar

[8] 8. Skorniakov, L. A., Alternative division rings (Russian), Ukrain. Mat. Z. 2 (1950), 70–85. Google Scholar

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