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On normal integral bases of local fields. (English) Zbl 0595.12007
The author gives a simple proof of the following theorem without using representation theory: any finite tamely ramified Galois extension of a local field has a normal integral basis. This theorem was obtained from Corollary 6.4 in R. G. Swan [Ann. Math., II. Ser. 71, 552-578 (1960; Zbl 0104.251)]. It was also proved by T. Tsukamoto [Sûgaku 11, 13-14 (1959) (Japanese)] containing the case of infinite residue field.
Reviewer: Zhang Xianke

MSC:
 11S15 Ramification and extension theory 11S20 Galois theory
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References:
 [1] Borevič, Z.I; Skopin, A.I, Extensions of a local field with normal basis for principal units, (), 48-55 · Zbl 0174.08803 [2] Fröhlich, A, Galois module structure of algebraic integers, () · Zbl 0501.12012 [3] Iwasawa, K, On Galois groups of local fields, Trans. amer. math. soc., 80, 448-469, (1955) · Zbl 0074.03101 [4] Lang, S, Algebraic number theory, (1970), Addison-Wesley Reading, Mass · Zbl 0211.38404 [5] Swan, R.G, Induced representations and projective modules, Ann. of math., 71, 552-578, (1960) · Zbl 0104.25102
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