Number fields
著者
書誌事項
Number fields
（Universitext）
Springer-Verlag, c1977
- : us
- : gw
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注記
"This book grew out of the lecture notes of a course ... at Yale University in the fall semester, 1972"
Bibliography: p. [272]
Includes indexes
内容説明・目次
- 巻冊次
-
: us ISBN 9780387902791
内容説明
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
目次
1: A Special Case of Fermat's Conjecture.- 2: Number Fields and Number Rings.- 3: Prime Decomposition in Number Rings.- 4: Galois Theory Applied to Prime Decomposition.- 5: The Ideal Class Group and the Unit Group.- 6: The Distribution of Ideals in a Number Ring.- 7: The Dedekind Zeta Function and the Class Number Formula.- 8: The Distribution of Primes and an Introduction to Class Field Theory.- Appendix 1: Commutative Rings and Ideals.- Appendix 2: Galois Theory for Subfields of C.- Appendix 3: Finite Fields and Rings.- Appendix 4: Two Pages of Primes.- Further Reading.- Index of Theorems.- List of Symbols.
- 巻冊次
-
: gw ISBN 9783540902799
内容説明
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields. It thus avoids local methods, for example, and presents proofs in a way that highlights the important parts of the arguments.
目次
- A special case of Fermat's conjecture
- number fields and number rings
- prime decomposition in number rings
- Galois theory applied to prime decomposition
- the ideal class group and the unit group
- the distribution of ideals in a number ring
- the Dedekind zeta function and the class number formula
- the distribution of primes and an introduction to class field theory.
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