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Synopsis
The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol. For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.
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Review
"Gives a highly readable introduction into class field theory ... clearly written and may be recommended to everybody interested in the subject." -- Zentralblatt fr Mathematik
"Provides a quick and self-contained introduction to the subject using only limited mathematical tools, hence it is accessible to a broader audience than most of the other texts on this topic." -- Mathematical Reviews
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- PublisherAmerican Mathematical Society
- Publication date2005
- ISBN 10 0821804294
- ISBN 13 9780821804292
- BindingHardcover
- LanguageEnglish
- Edition number2
- Number of pages276
- Rating
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Algebraic Number Fields (Graduate Studies in Mathematics, 7)
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Algebraic Number Fields. Second Edition (Graduate Studies in Mathematics, V. 7)
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Algebraic Number Fields
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American Mathematical Society, 1995
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Algebraic Number Fields (Graduate Studies in Mathematics, 7)
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ISBN 13: 9780821804292
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Algebraic Number Fields (Graduate Studies in Mathematics, 7)
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Algebraic Number Fields
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ISBN 13: 9780821804292
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Condition: Sehr gut. Zustand: Sehr gut - Gepflegter, sauberer Zustand. Aus der Auflösung einer renommierten Bibliothek. Kann Stempel beinhalten. | Seiten: 276 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 33432505/202
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Algebraic Number Fields
Published by
American Mathematical Society, 1995
ISBN 10: 0821804294
ISBN 13: 9780821804292
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Condition: Gut. Zustand: Gut - Gebrauchs- und Lagerspuren. Aus der Auflösung einer renommierten Bibliothek. Kann Stempel beinhalten. Fehlt: Schutzumschlag. | Seiten: 276 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 33432505/203
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Algebraic Number Fields (Graduate Studies in Mathematics, V. 7) (2nd ed) GSM/7
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Algebraic Number Fields (Graduate Studies in Mathematics, V. 7) (2nd ed) GSM/7
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ISBN 10: 0821804294
ISBN 13: 9780821804292
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Algebraic Number Fields
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