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Formal power series with cyclically ordered exponents

✍ Scribed by M. Giraudet; F. -V. Kuhlmann; G. Leloup

Publisher
Springer
Year
2005
Tongue
English
Weight
136 KB
Volume
84
Category
Article
ISSN
0003-889X

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πŸ“œ SIMILAR VOLUMES

Embedding ordered fields in formal power
Embedding ordered fields in formal power series fields
✍ F.-V. Kuhlmann; S. Kuhlmann; M. Marshall; M. Zekavat πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 198 KB

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.

Formal power series over Cartesian group
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We introduce formal power series over Cartesian groups on arbitrary, ordered loops, and show that, under a weak additional hypothesis, their spaces of orderings (in the sense of M. Marshall) are as in the classical case. In particular, we obtain that any classical space of orderings can be realized

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CM-Fields with Cyclic Ideal Class Groups of 2-Power Orders
✍ StΓ©phane Louboutin πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 298 KB

We prove that there are only finitely many CM-fields N with cyclic ideal class groups of 2-power orders such that the complex conjugation is the square of some automorphism of N. Since their actual determination would be too difficult, we only content ourselves with the determination of the nonquadr