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＜図書＞
A course in Galois theory
| 責任表示 | D.J.H. Garling |
|---|---|
| データ種別 | 図書 |
| 出版情報 | Cambridge [Cambridgeshire] ; New York : Cambridge University Press , 1986 |
| 本文言語 | 英語 |
| 大きさ | viii, 167 p. : ill. ; 24 cm |
| 概要 | Galois theory is one of the most beautiful branches of mathematics. By synthesising the techniques of group theory and field theory it provides a complete answer to the problem of the solubility of po...ynomials by radicals: that is, the problem of determining when and how a polynomial equation can be solved by repeatedly extracting roots and using elementary algebraic operations. This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to the subject. The work begins with an elementary discussion of groups, fields and vector spaces, and then leads the reader through such topics as rings, extension fields, ruler-and-compass constructions, to automorphisms and the Galois correspondence. By these means, the problem of the solubility of polynomials by radicals is answered; in particular it is shown that not every quintic equation can be solved by radicals. Throughout, Dr Garling presents the subject not as something closed, but as one with many applications. In the final chapters, he discusses further topics, such as transcendence and the calculation of Galois groups, which indicate that there are many questions still to be answered. The reader is assumed to have no previous knowledge of Galois theory. Some experience of modern algebra is helpful, so that the book is suitable for undergraduates in their second or final years. There are over 200 exercises which provide a stimulating challenge to the reader. This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory. 続きを見る |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
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paperback | 理系図3F 数理独自 | GARL/20/1 | 1993 |
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023212000001000 |
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書誌詳細
| 別書名 | 異なりアクセスタイトル:Galois theory |
|---|---|
| 一般注記 | Includes index |
| 著者標目 | *Garling, D. J. H. |
| 件 名 | LCSH:Galois theory NDLSH:ガロアの理論 |
| 分 類 | LCC:QA171 DC19:512/.32 NDC8:411.73 |
| 書誌ID | 1001390475 |
| ISBN | 0521320771 |
| NCID | BA00323466 |
| 巻冊次 | hard covers ; ISBN:0521320771 paperback ; ISBN:0521312493 |
| 登録日 | 2009.11.02 |
| 更新日 | 2009.11.02 |