## A survey of modern algebra |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preface | 1 |

Rational Numbers and Fields | 33 |

Polynomials | 53 |

Copyright | |

79 other sections not shown

### Other editions - View all

### Common terms and phrases

affine transformation algebraic numbers automorphism basis Boolean algebra called canonical form cardinal number Chap characteristic roots characteristic vectors coefficients column commutative ring complex numbers conjugate contains coordinates Corollary cosets cyclic defined definition degree determined direct sum distributive law elements entries equivalent Euclidean EXERCISES factors field F formula function Galois group Gaussian integers given group G hence Hint homomorphism ideal identity implies induction integral domain inverse irreducible polynomial isomorphic lattice Lemma linear combination linear equations linear transformation linearly independent minimal polynomial modulo monic non-zero nonsingular normal subgroup one-one correspondence ordered domain ordered field orthogonal permutation plane polynomial f(x polynomial forms positive integers postulates Proof properties proves Theorem quadratic form quaternions quotient rational numbers real numbers relatively prime root field root of unity row-equivalent satisfies scalar Show solution spanned square subfield subset subspace symmetric Theorem 18 unique variables vector space Vn(F zero