## Algebraic number theory |

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### Contents

DEDEKIND DOMAINS AND ALGEBRAIC NUMBER THEORY | 1 |

LOCALIZATION AND MODULE INDICES | 15 |

ABSOLUTE VALUES AND COMPLETIONS | 27 |

Copyright | |

7 other sections not shown

### Common terms and phrases

A-module abelian extension abelian group absolute value algebraic number field algebraic number theory archimedian assertion automorphism Chapter class number coefficients complete conductor conjugates converges Corollary cyclic decomposition Dedekind domain defined definition denoted Dirichlet character discrete valuation ring discriminant divisor Eisenstein polynomial embedding equation example exercise extension of Q fact factor finite extension follows formula fractional ideal function Gal(K/Q Hence Hint homomorphism ideal class group integral closure irreducible isomorphism lemma Let F Let G Let K/Q Let L/K maximal ideal mod f module monic n-th root nonzero prime ideal norm normal extension normal integral basis notation odd prime p-adic field p-th prime element prime ideal primitive Proof Proposition Prove quotient field rational prime reader relatively prime residue field result ring of integers root of unity Section separable extension sequence subgroup suppose tamely ramified theorem totally ramified unique unit unramified unramified extension zero