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On the Isomorphisms of the Galois Groups of the Maximal Abelian Extensions of Imaginary Quadratic Fields
http://hdl.handle.net/10083/2243
http://hdl.handle.net/10083/22430fe22064-72de-456b-b165-9f634ed62aeb
名前 / ファイル | ライセンス | アクション |
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KJ00004829886.pdf (344.4 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2008-04-30 | |||||
タイトル | ||||||
タイトル | On the Isomorphisms of the Galois Groups of the Maximal Abelian Extensions of Imaginary Quadratic Fields | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Onabe, Midori
× Onabe, Midori |
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著者(ヨミ) | ||||||
識別子 | 70079 | |||||
識別子Scheme | WEKO | |||||
姓名 | オオナベ, ミドリ | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Let Q be the rational number field. For any algebraic number field k of finite degree over Q, we shall denote by A_k the maximal abelian extension of k and by Gal(A_k/k) the Galois group of A_k over k equipped with the Krull topology. The present paper exhibits some counterexamples to the following statement ; for two algebraic number fields k and k' of finite degree over Q, an isomorphism Gal(A_k/k)≅Gal(A_k'/k') of the Galois groups of maximal abelian extensions A_k/k and A_k'/k' implies an isomorphism k≅k'. In other words we shall see that Gal(A_k/k) does not determine the isomorphism class of an algebraic number field k. Furthermore, the counterexamples which we give will show that even if Gal(A_k/k) and Gal(A_k'/k') are isomorphic, the ideal class groups of k and k' are not necessarily isomorphic. | |||||
書誌情報 |
お茶の水女子大學自然科學報告 巻 27, 号 2, p. 155-161, 発行日 1976-12 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00298190 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00033958 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
形態 | ||||||
344397 bytes | ||||||
日本十進分類法 | ||||||
主題Scheme | NDC | |||||
主題 | 400 | |||||
出版者 | ||||||
出版者 | お茶の水女子大学 | |||||
資源タイプ | ||||||
内容記述タイプ | Other | |||||
内容記述 | 紀要論文 | |||||
資源タイプ・ローカル | ||||||
紀要論文 | ||||||
資源タイプ・NII | ||||||
Departmental Bulletin Paper | ||||||
資源タイプ・DCMI | ||||||
text | ||||||
資源タイプ・ローカル表示コード | ||||||
03 | ||||||
所属 | ||||||
Department of Mathematics, Faculty of Science, Ochanomizu University |