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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27910Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Yueh-Yi Huang | en |
| dc.contributor.author | 黃月邑 | zh_TW |
| dc.date.accessioned | 2021-06-12T18:27:25Z | - |
| dc.date.available | 2007-08-28 | |
| dc.date.copyright | 2007-08-28 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-08-09 | |
| dc.identifier.citation | [Ar] E. Artin and J. Tate, Class field theory, W. A. Benjamin, 1961.
[La] Serge Lang, Cyclotomis Fields I and II(cpmbined Second Edition), Springer-Verlag, 1990. [N1] Jurgen Neukirch, Class field theory, Springer-Verlag, 1986. [N2] Jurgen Neukirch, Algebraic number theory ; translated from the German by Norbert Schappacher , Springer, 1999. [Se] Jean-Pierre Serre, Classes des corps cyclotomic(d’apr`es K. Iwasawa), S´em. Bourbaki, 1958, Exp. no.174. [Ta] Ki-seng Tan, A Note on Iwasawa Theory, manuscript, 2005. [Wa] Lawrence C. Washington, I ntroduction to Cyclotomic Fields, Springer-Verlag, 1982. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27910 | - |
| dc.description.abstract | 1950年代，對於數域上的某些擴張，岩澤提出了計算其 class number 的理論。並討論了 cyclotomic 擴張及其他種類的伽羅瓦擴張。在這篇文章中，我將介紹這個定理並給出一些例子。 | zh_TW |
| dc.description.abstract | In the 1950's, Kenkichi Iwasawa had constructed his class number
formula on extensions of number fields. Iwasawa investigated towers of cyclotomic fields and other kinds of Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. In this thesis, I would like to introduce this theory and give some examples. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-12T18:27:25Z (GMT). No. of bitstreams: 1 ntu-96-R94221010-1.pdf: 221285 bytes, checksum: ae096476bfaedbedd5cddbe319b6a201 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Contents
Abstract in Chinese i Abstract ii Contents 1 1 Introduction 2 1.1 Notations and Basic Definitions . . . . . . . . . . . . . . . . . . . . . 3 2 The Iwasawa Algebra 4 2.1 Some Congruence Relations . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The Map f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 The Map g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 The Isomorphism and The Continuity . . . . . . . . . . . . . . . . . . 8 3 The Structure of -module 11 3.1 Finitely Generated Module . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Nakayama’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 The Cardinality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Iwasawa’s Theorem 16 4.1 The Main Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Bibliography 22 | |
| dc.language.iso | en | |
| dc.title | p無窮循環擴張上之依烏阿沙娃理論 | zh_TW |
| dc.title | Iwasawa Theory on Zp-extension | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳榮凱(Jung-Kai Chen),紀文鎮(Wen-Chen Chi),朱樺(Huah Chu) | |
| dc.subject.keyword | 依烏阿沙娃理論, | zh_TW |
| dc.subject.keyword | Iwasawa Theory, | en |
| dc.relation.page | 22 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-08-09 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-96-1.pdf Restricted Access | 216.1 kB | Adobe PDF |
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