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Abstrakty
There are many different definitions of the group of circular units of a real abelian field. The aim of this paper is to study their relations in the special case of a compositum k of real quadratic fields such that -1 is not a square in the genus field K of k in the narrow sense.
The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois group acts on C/(±C²) trivially (see [K, Lemma 2]).
Due to this key property we can easily compare different groups of circular units (see the conclusion of this paper).
The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois group acts on C/(±C²) trivially (see [K, Lemma 2]).
Due to this key property we can easily compare different groups of circular units (see the conclusion of this paper).
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
123-140
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-03-17
Twórcy
autor
- Department of Mathematics, Masaryk University, Janáčkovo Nám. 2a, 662 95 Brno, Czech Republic
Bibliografia
- [G] R. Gillard, Remarques sur les unités cyclotomiques et les unités elliptiques, J. Number Theory 11 (1979), 21-48.
- [K] R. Kučera, On the Stickelberger ideal and circular units of a compositum of quadratic fields, preprint.
- [L] G. Lettl, A note on Thaine's circular units, J. Number Theory 35 (1990), 224-226.
- [S] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234.
- [W] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-aav67i2p123bwm