On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$
Mathematica Bohemica (2023)
- Volume: 148, Issue: 2, page 237-242
- ISSN: 0862-7959
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topChems-Eddin, Mohamed Mahmoud. "On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$." Mathematica Bohemica 148.2 (2023): 237-242. <http://eudml.org/doc/299572>.
@article{Chems2023,
abstract = {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 $\mathbb \{Q\}\big (\sqrt 2, \sqrt \{p\}, \sqrt \{q\}, \sqrt \{-\ell \} \big )$.},
author = {Chems-Eddin, Mohamed Mahmoud},
journal = {Mathematica Bohemica},
language = {eng},
number = {2},
pages = {237-242},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On units of some fields of the form $\mathbb \{Q\}\big (\sqrt 2, \sqrt \{p\}, \sqrt \{q\}, \sqrt \{-l\}\big )$},
url = {http://eudml.org/doc/299572},
volume = {148},
year = {2023},
}
TY - JOUR
AU - Chems-Eddin, Mohamed Mahmoud
TI - On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 2
SP - 237
EP - 242
AB - 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 $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-\ell } \big )$.
LA - eng
UR - http://eudml.org/doc/299572
ER -
References
top- Azizi, A., Unités de certains corps de nombres imaginaires et abéliens sur $\mathbb{Q}$, Ann. Sci. Math. Qué. 23 (1999), 15-21 French. (1999) Zbl1041.11072MR1721726
- 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. (2021)
- Chems-Eddin, M. M., 10.1007/s10998-021-00402-0, Period. Math. Hung. 84 (2022), 235-249. (2022) MR4423478DOI10.1007/s10998-021-00402-0
- Chems-Eddin, M. M., Azizi, A., Zekhnini, A., 10.1007/s40590-021-00329-z, Bol. Soc. Mat. Mex., III. Ser. 27 (2021), Article ID 24, 16 pages. (2021) Zbl07342807MR4220815DOI10.1007/s40590-021-00329-z
- Chems-Eddin, M. M., Zekhnini, A., Azizi, A., 10.3906/mat-2003-117, Turk. J. Math. 44 (2020), 1466-1483. (2020) Zbl1455.11140MR4122918DOI10.3906/mat-2003-117
- Kubota, T., 10.1017/S0027763000000088, Nagoya Math. J. 10 (1956), 65-85 German. (1956) Zbl0074.03001MR0083009DOI10.1017/S0027763000000088
- 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. (1925)
- 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 . (1966) Zbl0158.30103MR0214565
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