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Title: Annihilators of the class group of a compositum of quadratic fields (English)
Author: Herman, Jan
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 49
Issue: 4
Year: 2013
Pages: 209-222
Summary lang: English
Category: math
Summary: This paper is devoted to a construction of new annihilators of the ideal class group of a tamely ramified compositum of quadratic fields. These annihilators are produced by a modified Rubin’s machinery. The aim of this modification is to give a stronger annihilation statement for this specific type of fields. (English)
Keyword: annihilators
Keyword: class group
Keyword: circular (cyclotomic) units
Keyword: compositum of quadratic fields
MSC: 11G16
MSC: 11R20
MSC: 11R27
MSC: 11R29
idZBL: Zbl 1299.11079
idMR: MR3159311
DOI: 10.5817/AM2013-4-209
Date available: 2014-01-16T11:12:26Z
Last updated: 2015-03-19
Stable URL:
Reference: [1] Greither, C., Kučera, R.: Annihilators for the class group of a cyclic field of prime power degree.Acta Arith. 112 (2) (2004), 177–198. Zbl 1065.11089, MR 2051376, 10.4064/aa112-2-6
Reference: [2] Kučera, R.: On the class number of a compositum of real quadratic fields: an approach via circular units.Funct. Approx. Comment. Math. 39 (2008), 179–189. Zbl 1225.11141, MR 2490724, 10.7169/facm/1229696569
Reference: [3] Lambek, J.: Lectures on rings and modules.3rd ed., Chelsea Publishing Co., New York, 1988.
Reference: [4] Rubin, K.: Global units and ideal class groups.Invent. Math. 89 (1987), 511–526. Zbl 0628.12007, 10.1007/BF01388983
Reference: [5] Sinnott, W.: On the Stickelberger ideal and the circular units of an abelian field.Invent. Math. 62 (1980), 181–234. Zbl 0465.12001, 10.1007/BF01389158
Reference: [6] Thaine, F.: On the ideal class groups of real abelian number fields.Ann. of Math. (2) 128 (1988), 1–18. Zbl 0665.12003


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