Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Algebraic Number Fields: Second Edition
 
Gerald J. Janusz University of Illinois, Urbana, IL
Algebraic Number Fields
Hardcover ISBN:  978-0-8218-0429-2
Product Code:  GSM/7
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Sale Price: $64.35
eBook ISBN:  978-1-4704-1141-1
Product Code:  GSM/7.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Hardcover ISBN:  978-0-8218-0429-2
eBook: ISBN:  978-1-4704-1141-1
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
Sale Price: $119.60 $91.98
Algebraic Number Fields
Click above image for expanded view
Algebraic Number Fields: Second Edition
Gerald J. Janusz University of Illinois, Urbana, IL
Hardcover ISBN:  978-0-8218-0429-2
Product Code:  GSM/7
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Sale Price: $64.35
eBook ISBN:  978-1-4704-1141-1
Product Code:  GSM/7.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Sale Price: $55.25
Hardcover ISBN:  978-0-8218-0429-2
eBook ISBN:  978-1-4704-1141-1
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
Sale Price: $119.60 $91.98
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 71996; 276 pp
    MSC: 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 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.

    Readership

    Mathematics 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 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 71996; 276 pp
MSC: 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 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.

Readership

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 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.