## First course in algebra and number theory |

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### Contents

Rings and Domains | 90 |

Congruences and Polynomials | 210 |

Groups | 380 |

Copyright | |

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### Common terms and phrases

abelian addition and multiplication arbitrary associative law axioms Chinese remainder theorem coefficients common divisor commutative law commutative ring complex numbers Consider course cycle cyclic group define definition denote disjoint divides division algorithm equal equation Euclidean algorithm example exists exponent expression fact factorization finite number given greatest common divisor group G homomorphism identity induction injective integral domain inverse irreducible isomorphism left cosets linear congruence Map(A mapping monic nonzero element normal subgroup notation odd prime ordered domain permutation polynomial f(x polynomial of degree positive integer primitive root primitive root mod Problem properties Proposition prove quadratic quadratic residue reader real numbers relatively prime residue classes result ring with unity solution solve subgroup of G subring subset Suppose surjective symbol theorem unique unit vp(a vp(b words write zero-divisor