Extensions of normal bases and completely basic fields
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- by Carl C. Faith
- Trans. Amer. Math. Soc. 85 (1957), 406-427
- DOI: https://doi.org/10.1090/S0002-9947-1957-0087632-7
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Erratum: Trans. Amer. Math. Soc. 89 (1958), 559-559.
References
- A. A. Albert, Modern higher algebra, Chicago, 1937, pp. 146-216.
- Emil Artin, Galois Theory, Notre Dame Mathematical Lectures, no. 2, University of Notre Dame, Notre Dame, Ind., 1942. Edited and supplemented with a section on applications by Arthur N. Milgram. MR 0006974 —, Linear mappings and the existence of a normal basis, Studies and Essays presented to R. Courant on his 60th birthday, New York, 1948. N. Bourbaki, Éléments de mathématique, Livre II-Algèbre, Chapitres, IV and V, Actualités Scientifiques et Industrielles, no. 1102.
- J. W. S. Cassels and G. E. Wall, The normal basis theorem, J. London Math. Soc. 25 (1950), 259–264. MR 37284, DOI 10.1112/jlms/s1-25.4.259 M. Deuring, Galoissche Theorie und Darstellungstheorie, Math. Ann. vol. 107 (1932) p. 140. C. C. Faith, Normal extensions in which every element with nonzero trace is a normal basis element, unpublished.
- Tadasi Nakayama, On Frobeniusean algebras. II, Ann. of Math. (2) 42 (1941), 1–21. MR 4237, DOI 10.2307/1968984
- Sam Perlis, Normal bases of cyclic fields of prime-power degree, Duke Math. J. 9 (1942), 507–517. MR 7005
- Ruth Stauffer, The Construction of a Normal Basis in a Separable Normal Extension Field, Amer. J. Math. 58 (1936), no. 3, 585–597. MR 1507183, DOI 10.2307/2370977
Bibliographic Information
- © Copyright 1957 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 85 (1957), 406-427
- MSC: Primary 09.3X
- DOI: https://doi.org/10.1090/S0002-9947-1957-0087632-7
- MathSciNet review: 0087632