Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
annihilators; class group; circular (cyclotomic) units; compositum of quadratic fields
annihilators; class group; circular (cyclotomic) units; compositum of quadratic fields
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.
References:
[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. DOI 10.4064/aa112-2-6 | MR 2051376 | Zbl 1065.11089
[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. DOI 10.7169/facm/1229696569 | MR 2490724 | Zbl 1225.11141
[3] Lambek, J.: Lectures on rings and modules. 3rd ed., Chelsea Publishing Co., New York, 1988.
[4] Rubin, K.: Global units and ideal class groups. Invent. Math. 89 (1987), 511–526. DOI 10.1007/BF01388983 | Zbl 0628.12007
[5] Sinnott, W.: On the Stickelberger ideal and the circular units of an abelian field. Invent. Math. 62 (1980), 181–234. DOI 10.1007/BF01389158 | Zbl 0465.12001
[6] Thaine, F.: On the ideal class groups of real abelian number fields. Ann. of Math. (2) 128 (1988), 1–18. Zbl 0665.12003
Search
Partner of
