On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2)
We study the capitulation of the 2-ideal classes of the field k =Q(\sqrt{p_1p_2q}, \sqrt{-1}), where p_1\equiv p_2\equiv-q\equiv1 \pmod 4 are different primes, in its three quadratic extensions contained in its absolute genus field k^{*} whenever the 2-class group of $\kk$ is of type $(2, 2, 2)$.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2019-03-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/36793 |
| _version_ | 1797633482290102272 |
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| author | Abdelmalek Azizi Abdelkader Zekhnini Mohammed Taous |
| author_facet | Abdelmalek Azizi Abdelkader Zekhnini Mohammed Taous |
| author_sort | Abdelmalek Azizi |
| collection | DOAJ |
| description | We study the capitulation of the 2-ideal classes of the field k =Q(\sqrt{p_1p_2q}, \sqrt{-1}), where p_1\equiv p_2\equiv-q\equiv1 \pmod 4 are different primes, in its three quadratic extensions contained in its absolute genus field k^{*} whenever the 2-class group of $\kk$ is of type $(2, 2, 2)$. |
| first_indexed | 2024-03-11T11:54:38Z |
| format | Article |
| id | doaj.art-35b313a76b4d439b9a310c0ae3f9415b |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:54:38Z |
| publishDate | 2019-03-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-35b313a76b4d439b9a310c0ae3f9415b2023-11-08T20:07:44ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-03-0138410.5269/bspm.v38i4.36793On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2)Abdelmalek Azizi0Abdelkader Zekhnini1Mohammed Taous2Mohammed First University Sciences Faculty Mathematics DepartmentMohammed First university Pluridisciplinary Faculty of NadorMoulay Ismail University Sciences and Techniques Faculty Mathematics DepartmentWe study the capitulation of the 2-ideal classes of the field k =Q(\sqrt{p_1p_2q}, \sqrt{-1}), where p_1\equiv p_2\equiv-q\equiv1 \pmod 4 are different primes, in its three quadratic extensions contained in its absolute genus field k^{*} whenever the 2-class group of $\kk$ is of type $(2, 2, 2)$.https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/36793absolute genus fieldsfundamental systems of units$2$-class groupcapitulationquadratic fieldsbiquadratic fields |
| spellingShingle | Abdelmalek Azizi Abdelkader Zekhnini Mohammed Taous On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2) Boletim da Sociedade Paranaense de Matemática absolute genus fields fundamental systems of units $2$-class group capitulation quadratic fields biquadratic fields |
| title | On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2) |
| title_full | On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2) |
| title_fullStr | On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2) |
| title_full_unstemmed | On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2) |
| title_short | On the capitulation of the $2$-ideal classes of the field Q(\sqrt{pq_1q_2}, i) of type (2, 2, 2) |
| title_sort | on the capitulation of the 2 ideal classes of the field q sqrt pq 1q 2 i of type 2 2 2 |
| topic | absolute genus fields fundamental systems of units $2$-class group capitulation quadratic fields biquadratic fields |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/36793 |
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