In the paper it is shown how an embedding of an ordered ΓΏeld F into a formal power series ΓΏeld can be extended canonically to an embedding of any simple extension F(y) of F. Properties of the extended embedding are studied in detail. Several applications are given.
Elementary embeddings of fields of power series
β Scribed by Abraham Robinson
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 550 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let K be a finite tamely ramified extension of Q p and let L/K be a totally ramified (Z/p n Z)-extension. Let L be a uniformizer for L, let be a generator for Gal(L/K), and let f (X) be an element of O K [X] such that ( L ) = f ( L ). We show that the reduction of f (X) modulo the maximal ideal of O
The Brauer-Witt Theorem states that every Schur algebra over a ΓΏeld K is Brauer equivalent to a cyclotomic algebra. A central conjecture on the projective Schur group of a ΓΏeld is the analogue of this theorem, which asserts that every projective Schur algebra over a ΓΏeld K is Brauer equivalent to a