We investigate the trace form tr : In particular, we study 2-extensions of degree F 16. Using some reduction theorems, these results yield a classification of nearly all trace forms of Galois extensions of degree F 31. Finally, we study the trace form of a cyclotomic extension and of its maximal re
The Galois structure of the trace form in extensions of odd prime degree
β Scribed by B Erez
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 432 KB
- Volume
- 118
- Category
- Article
- ISSN
- 0021-8693
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Let k be a Galois extension of Q with [k : Q]=d 2. The purpose of this paper is to give an upper bound for the least prime which does not split completely in k in terms of the degree d and the discriminant 2 k . Our estimate improves on the bound given by Lagarias et al. [3]. We note, however, that
Let p be an odd prime and n a positive integer and let k be a field of Ε½ . r p and let r denote the largest integer between 0 and n such that K l k s p Ε½ . r r r k , where denotes a primitive p th root of unity. The extension Krk is p p separable, but not necessarily normal and, by Greither and Pa