Hardcover ISBN:  9780821804292 
Product Code:  GSM/7 
List Price:  $99.00 
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AMS Member Price:  $79.20 
eBook ISBN:  9781470411411 
Product Code:  GSM/7.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821804292 
eBook: ISBN:  9781470411411 
Product Code:  GSM/7.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 
Hardcover ISBN:  9780821804292 
Product Code:  GSM/7 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470411411 
Product Code:  GSM/7.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821804292 
eBook ISBN:  9781470411411 
Product Code:  GSM/7.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 

Book DetailsGraduate Studies in MathematicsVolume: 7; 1996; 276 ppMSC: Primary 11
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 as 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 yearlong course in algebraic number theory; the first three chapters would be suitable for a onesemester course. It is also very suitable for independent study.
ReadershipMathematics graduate students and faculty.

Table of Contents

Chapters

Chapter I. Subrings of fields

Chapter II. Complete fields

Chapter III. Decomposition groups and the Artin map

Chapter IV. Analytic methods and Ray classes

Chapter V. Class field theory

Chapter VI. Quadratic fields

Appendix


Reviews

Gives a highly readable introduction into class field theory ... clearly written and may be recommended to everybody interested in the subject.
Zentralblatt MATH 
Provides a quick and selfcontained 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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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 as 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 yearlong course in algebraic number theory; the first three chapters would be suitable for a onesemester course. It is also very suitable for independent study.
Mathematics graduate students and faculty.

Chapters

Chapter I. Subrings of fields

Chapter II. Complete fields

Chapter III. Decomposition groups and the Artin map

Chapter IV. Analytic methods and Ray classes

Chapter V. Class field theory

Chapter VI. Quadratic fields

Appendix

Gives a highly readable introduction into class field theory ... clearly written and may be recommended to everybody interested in the subject.
Zentralblatt MATH 
Provides a quick and selfcontained 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