On units of some fields of the form ( 2 , p , q , - l )

Mohamed Mahmoud Chems-Eddin

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 2, page 237-242
  • ISSN: 0862-7959

Abstract

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Let p 1 ( mod 8 ) and q 3 ( mod 8 ) be two prime integers and let { - 1 , p , q } be a positive odd square-free integer. Assuming that the fundamental unit of ( 2 p ) has a negative norm, we investigate the unit group of the fields ( 2 , p , q , - ) .

How to cite

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Chems-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 $p\equiv 1\hspace\{4.44443pt\}(\@mod \; 8)$ and $q\equiv 3\hspace\{4.44443pt\}(\@mod \; 8)$ be two prime integers and let $\ell \notin \lbrace -1, p, q\rbrace $ 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},
keywords = {multiquadratic number field; unit group; fundamental system of units},
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 $p\equiv 1\hspace{4.44443pt}(\@mod \; 8)$ and $q\equiv 3\hspace{4.44443pt}(\@mod \; 8)$ be two prime integers and let $\ell \notin \lbrace -1, p, q\rbrace $ 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
KW - multiquadratic number field; unit group; fundamental system of units
UR - http://eudml.org/doc/299572
ER -

References

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  1. Azizi, A., Unités de certains corps de nombres imaginaires et abéliens sur , Ann. Sci. Math. Qué. 23 (1999), 15-21 French. (1999) Zbl1041.11072MR1721726
  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. (2021) 
  3. Chems-Eddin, M. M., 10.1007/s10998-021-00402-0, Period. Math. Hung. 84 (2022), 235-249. (2022) MR4423478DOI10.1007/s10998-021-00402-0
  4. 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
  5. 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
  6. Kubota, T., 10.1017/S0027763000000088, Nagoya Math. J. 10 (1956), 65-85 German. (1956) Zbl0074.03001MR0083009DOI10.1017/S0027763000000088
  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 9999JFM99999 51.0123.05. (1925) 
  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 9999MR99999 0214565 . (1966) Zbl0158.30103MR0214565

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