# Different groups of circular units of a compositum of real quadratic fields

Acta Arithmetica (1994)

- Volume: 67, Issue: 2, page 123-140
- ISSN: 0065-1036

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topRadan Kučera. "Different groups of circular units of a compositum of real quadratic fields." Acta Arithmetica 67.2 (1994): 123-140. <http://eudml.org/doc/206622>.

@article{RadanKučera1994,

abstract = {
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).
},

author = {Radan Kučera},

journal = {Acta Arithmetica},

keywords = {abelian field; cyclotomic unit; real quadratic fields; circular units},

language = {eng},

number = {2},

pages = {123-140},

title = {Different groups of circular units of a compositum of real quadratic fields},

url = {http://eudml.org/doc/206622},

volume = {67},

year = {1994},

}

TY - JOUR

AU - Radan Kučera

TI - Different groups of circular units of a compositum of real quadratic fields

JO - Acta Arithmetica

PY - 1994

VL - 67

IS - 2

SP - 123

EP - 140

AB -
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).

LA - eng

KW - abelian field; cyclotomic unit; real quadratic fields; circular units

UR - http://eudml.org/doc/206622

ER -

## References

top- [G] R. Gillard, Remarques sur les unités cyclotomiques et les unités elliptiques, J. Number Theory 11 (1979), 21-48. Zbl0405.12008
- [K] R. Kučera, On the Stickelberger ideal and circular units of a compositum of quadratic fields, preprint. Zbl0840.11044
- [L] G. Lettl, A note on Thaine's circular units, J. Number Theory 35 (1990), 224-226. Zbl0705.11064
- [S] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. Zbl0465.12001
- [W] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982. Zbl0484.12001

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