Number fields
著者
書誌事項
Number fields
（Universitext）
Springer-Verlag, c1977(1995 printing)
3rd correcting printing
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注記
"Third corrected printing"--T.p. verso
Includes bibliographical references (p. [272]) and indexes
内容説明・目次
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.
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