## Abstract algebra |

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#### Best Intro Book

User Review - Anonymous - BordersThis book is well written. It covers most of the materials needed for an introduction to Abstract Algebra. The notations used are reader friendly. This book is comparatively cheaper than other Abstract Algebra book. This is a must have for all who's taking an Abstract Algebra class. Read full review

### Contents

THE BASIC NUMBER SYSTEMS | 32 |

DECOMPOSITIONS OF INTEGERS | 82 |

DIOPHANTINE PROBLEMS | 121 |

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### Common terms and phrases

Abelian group addition and multiplication algebraic automorphism Axiom binary operations canonical basis characteristic polynomial classes Cn(F column common factor commutative components conclude congruence consider contains Corollary correspondence cosets cyclic defined Definition denoted Describe Determine diagonal divisors of zero element of G elementary row operations equal equation equivalence relation Example expressible Find finite GF(pn group G Hence homomorphic image ideals of QD(m identity element implies induction hypothesis integral domain irreducible irreducible polynomial isomorphic Lemma linear transformation linearly independent mathematical matrix minimal modulo monic natural numbers nonsingular nonzero elements normal subgroup number system obtain one-to-one mapping operation table pair positive integers Problem proof properties prove quadratic quotient rank rational integers rational number reduced row echelon relatively prime ring row echelon form semigroup Show solution splitting field subfield subgroup of G subgroup of order subring subset vector space Vn(F yields zero mod zeros modulo