Local fields

著者

• Cassels, J. W. S. (John William Scott)

書誌事項

Local fields

J.W.S. Cassels

（London Mathematical Society student texts, 3）

Cambridge University Press, 1986

• : hardcover
• : pbk

注記

Includes bibliographical references (p. 352-357) and index

内容説明・目次

内容説明

The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural concepts, which often provide remarkably easy solutions to complex problems, are not as familiar as they should be. This book, based on postgraduate lectures at Cambridge, is meant to rectify this situation by providing a fairly elementary and self-contained introduction to local fields. After a general introduction, attention centres on the p-adic numbers and their use in number theory. There follow chapters on algebraic number theory, diophantine equations and on the analysis of a p-adic variable. This book will appeal to undergraduates, and even amateurs, interested in number theory, as well as to graduate students.

目次

• Preface
• Leitfaden
• Notational conventions
• 1. Introduction
• 2. General properties
• 3. Archimedean valuations
• 4. Non archimedean valuations
• 5. Embedding theorem
• 6. Transcendental extensions
• 7. Algebraic extensions
• 8. p-adic fields
• 9. Algebraic extensions
• 10. Algebraic number fields
• 11. Diophantine equations
• 12. Advanced analysis
• 13. A theorem of Borel and work
• Appendices
• References
• Index.

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詳細情報

• NII書誌ID(NCID): BA0035500X
• ISBN:
  • 0521304849
  • 0521315255
• LCCN: 85047934
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge [Cambridgeshire] ; New York
• ページ数/冊数: xiv, 360 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA247
  • DC19 : 512/.3
  • NDC8 : 411.73
• 件名:
  • LCSH : Local fields (Algebra)
  • NDLSH : 体(数学)
• 親書誌ID:
  • BA00194352