| Title:
|
On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$ (English) |
| Author:
|
Chems-Eddin, Mohamed Mahmoud |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
237-242 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p\equiv 1\pmod {8}$ and $q\equiv 3\pmod 8$ be two prime integers and let $\ell \not \in \{-1, p, q\}$ be a positive odd square-free integer. Assuming that the fundamental unit of $\mathbb {Q}\big (\sqrt {2p}\big ) $ has a negative norm, we investigate the unit group of the fields $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-\ell } \big )$. (English) |
| Keyword:
|
multiquadratic number field |
| Keyword:
|
unit group |
| Keyword:
|
fundamental system of units |
| MSC:
|
11R04 |
| MSC:
|
11R27 |
| MSC:
|
11R29 |
| MSC:
|
11R37 |
| idZBL:
|
Zbl 07729575 |
| idMR:
|
MR4585579 |
| DOI:
|
10.21136/MB.2022.0128-21 |
| . |
| Date available:
|
2023-05-04T17:59:21Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151687 |
| . |
| Reference:
|
[1] Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur $\mathbb{Q}$.Ann. Sci. Math. Qué. 23 (1999), 15-21 French. Zbl 1041.11072, MR 1721726 |
| Reference:
|
[2] Chems-Eddin, M. M.: Arithmetic of some real triquadratic fields: Units and 2-class groups.Available at https://arxiv.org/abs/2108.04171v1 (2021), 32 pages. |
| Reference:
|
[3] Chems-Eddin, M. M.: Unit groups of some multiquadratic number fields and 2-class groups.Period. Math. Hung. 84 (2022), 235-249. MR 4423478, 10.1007/s10998-021-00402-0 |
| Reference:
|
[4] Chems-Eddin, M. M., Azizi, A., Zekhnini, A.: Unit groups and Iwasawa lambda invariants of some multiquadratic number fields.Bol. Soc. Mat. Mex., III. Ser. 27 (2021), Article ID 24, 16 pages. Zbl 07342807, MR 4220815, 10.1007/s40590-021-00329-z |
| Reference:
|
[5] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: Units and 2-class field towers of some multiquadratic number fields.Turk. J. Math. 44 (2020), 1466-1483. Zbl 1455.11140, MR 4122918, 10.3906/mat-2003-117 |
| Reference:
|
[6] Kubota, T.: Über den bizyklischen biquadratischen Zahlkörper.Nagoya Math. J. 10 (1956), 65-85 German. Zbl 0074.03001, MR 0083009, 10.1017/S0027763000000088 |
| Reference:
|
[7] Varmon, J.: Über Abelsche Körper, deren alle Gruppeninvarianten aus einer Primzahl bestehen, und über Abelsche Körper als Kreiskörper.Hakan Ohlssons Boktryckeri, Lund (1925), German \99999JFM99999 51.0123.05. |
| Reference:
|
[8] Wada, H.: On the class number and the unit group of certain algebraic number fields.J. Fac. Sci, Univ. Tokyo, Sect. I 13 (1966), 201-209 \99999MR99999 0214565 . Zbl 0158.30103, MR 0214565 |
| . |
