On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$
Let $p\equiv1\pmod8$ and $q\equiv3\pmod8$ 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(\sqrt2, \sq...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2023-07-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/148/2/mb148_2_7.pdf |
| _version_ | 1797837599208898560 |
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| author | Mohamed Mahmoud Chems-Eddin |
| author_facet | Mohamed Mahmoud Chems-Eddin |
| author_sort | Mohamed Mahmoud Chems-Eddin |
| collection | DOAJ |
| description | Let $p\equiv1\pmod8$ and $q\equiv3\pmod8$ 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 $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell} \big)$. |
| first_indexed | 2024-04-09T15:28:24Z |
| format | Article |
| id | doaj.art-d1d99fa061fb4c1687ecb0cfe35ff012 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-04-09T15:28:24Z |
| publishDate | 2023-07-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-d1d99fa061fb4c1687ecb0cfe35ff0122023-04-28T12:19:40ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362023-07-01148223724210.21136/MB.2022.0128-21MB.2022.0128-21On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$Mohamed Mahmoud Chems-EddinLet $p\equiv1\pmod8$ and $q\equiv3\pmod8$ 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 $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell} \big)$.http://mb.math.cas.cz/full/148/2/mb148_2_7.pdf multiquadratic number field unit group fundamental system of units |
| spellingShingle | Mohamed Mahmoud Chems-Eddin On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$ Mathematica Bohemica multiquadratic number field unit group fundamental system of units |
| title | On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$ |
| title_full | On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$ |
| title_fullStr | On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$ |
| title_full_unstemmed | On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$ |
| title_short | On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$ |
| title_sort | on units of some fields of the form mathbb q big sqrt2 sqrt p sqrt q sqrt l big |
| topic | multiquadratic number field unit group fundamental system of units |
| url | http://mb.math.cas.cz/full/148/2/mb148_2_7.pdf |
| work_keys_str_mv | AT mohamedmahmoudchemseddin onunitsofsomefieldsoftheformmathbbqbigsqrt2sqrtpsqrtqsqrtlbig |