## Number theory II: algebraic number theoryFrom the reviews: ..". The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." "Monatshefte fuer Mathematik, 1994" ..". Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." "Medelingen van het" "wiskundig genootschap, 1995" |

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### Contents

Preface | 7 |

2 Rings with Divisor Theory | 22 |

4 Valuations | 45 |

Copyright | |

17 other sections not shown

### Common terms and phrases

abelian extension abelian group algebraic number ﬁeld arbitrary Artin Artin L-functions automorphism called Chap class ﬁeld theory closed subgroup cohomology complex conductor conjecture corresponding cyclic cyclotomic ﬁelds decomposition Dedekind ring deﬁned deﬁnition denotes Dirichlet discriminant divisor theory exact sequence Example extension of Q field ﬁnd ﬁnite ﬁnite extension ﬁnite group ﬁnite normal extension ﬁrst ﬁxed following theorem G-module Galois group global ﬁelds group G Hasse Hecke character Hence Hilbert homomorphism ideal class group idele imaginary-quadratic implies induces inﬁnite integers integral closure inverse irreducible isomorphism L-functions Lemma Let f Let G Let L/K Main reference module morphism natural number norm symbol normal extension normal subgroup number theory polynomial prime divisors prime element prime ideal prime number pro-p-group proﬁnite group proof of Theorem Proposition ramiﬁed reciprocity law representation residue resp roots of unity Shafarevich simple algebra subgroup of G sufﬁcient Theorem topological trivial unramiﬁed valuation