Galois theory

著者

• Stewart, Ian Nicholas

書誌事項

Galois theory

Ian Stewart

（Chapman & Hall/CRC mathematics）

Chapman & Hall/CRC, c2004

3rd ed

• : pbk

注記

Includes bibliographical references and index

内容説明・目次

内容説明

Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches. To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.

目次

Historical Introduction Classical Algebra The Fundamental Theorem of Algebra Factorization of Polynomials Field Extensions Simple Extensions The Degree of an Extension Ruler-and-Compass Constructions The Idea Behind Galois Theory Normality and Separability Counting Principles Field Automorphisms The Galois Correspondence A Worked Example Solubility and Simplicity Solution by Radicals Abstract Rings and Fields Abstract Field Extensions The General Polynomial Regular Polygons Finite Fields Circle Division Calculating Galois Groups Algebraically Closed Fields Transcendental Numbers References Index

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詳細情報

• NII書誌ID(NCID): BA63389866
• ISBN:
  • 1584883936
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton
• ページ数/冊数: xxxv, 288 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA214
  • DC : 512/.32
• 件名:
  • LCSH : Galois theory
• 親書誌ID:
  • BA50255823