| 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:
|
http://hdl.handle.net/10338.dmlcz/143546 |
| . |
| 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 |
| . |
