zbMATH — the first resource for mathematics

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

11S15 Ramification and extension theory
11S20 Galois theory
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.