## Algorithmic Algebraic Number TheoryNow in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value. |

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### Contents

III | 1 |

IV | 4 |

V | 7 |

VI | 13 |

VII | 15 |

VIII | 23 |

IX | 29 |

X | 37 |

XXIX | 313 |

XXX | 327 |

XXXI | 329 |

XXXII | 336 |

XXXIII | 343 |

XXXIV | 350 |

XXXV | 372 |

XXXVI | 377 |

### Common terms and phrases

abelian algebraic number field algebraically ordered algorithm apply assume chapter class field class group class number coefficients computation conjugates construction contains corresponding Dedekind ring defined Definition denotes entire ring equivalent example exercise exponent exponential valuation factorization field F finite extension finite number follows fractional ideals fundamental units Galois group G Hence Hermite normal form homomorphism idempotents implies integral closure integral ideal irreducible polynomial isomorphic kash Krull valuation Lemma linear matrix representation maximal ideal maximal order method minimal splitting modulo monic non-constant polynomial monic polynomial multiplication natural number nilpotent non-zero divisor non-zero element non-zero ideal non-zero prime ideal norm number theory obtain presentation prime ideal prime number primitive idempotents principal ideal quadratic quotient ring R-basis R-module rational integers root of unity satisfying separable polynomial solution Step subfield subgroup subring subset theorem TU(R unital commutative ring universal splitting ring vectors yields zero