## Integral Bases |

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### Contents

CHAP page I Introduction and Summary | 1 |

Dedekinds Theory of Ideal Numbers | 7 |

HI Canonical Form of an Integral Basis | 9 |

Copyright | |

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### Common terms and phrases

algebraic integers algebraic numbers argument belongs CHAPTER complex integer compound modulus congruence contains cubic field cyclotomic field Dedekind degree g determine diagram of squares discriminant divides Fermat's last theorem field of algebraic form the stem Further hasp Hence highly divisible ideal numbers integral basis integral polynomial irreducible divisors mod irreducible equation irreducible mod irreducible polynomial isobaric mod least lower rank marked node mod pj modd modp modp2 modulus of order notation number-field numerical example obtained partial basis prime factors prime ideal factors prime ideals attached prime number product of irreducible proved quadratic field rational integers rational integral values readily seen relative field relative-field represented by nodes respectively roots s)th term satisfied second dissection separates the prime shewn shews slant solution super-field terms represented theorem third dissection unique positive integers uniquely expressible unity w(zy whence