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Algebraic Number Fields
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This book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are included. Suitable for graduate students and faculty interested in number theory, this book can also serve as a textbook for a one term course that introduces algebraic number theory and a second course on the basic theory of class fields of algebraic number fields.This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important...
This book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are included. Suitable for graduate students and faculty interested in number theory, this book can also serve as a textbook for a one term course that introduces algebraic number theory and a second course on the basic theory of class fields of algebraic number fields.
This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. This book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. This book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.