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Abstract Algebra by John A. Beachy and William D. Blair

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books.

Abstract Algebra written by John A. Beachy and William D. Blair . This is an other great mathematics book cover the following topics.

  • Introduction
    Some history, Biographies (from the MacTutor History of Mathematics archives), Some help with logic and proofs, Links to some algebra sites

  • Chapter 1: INTEGERS
    Divisors, Primes, Congruences, Integers Modulo n, Review

  • Chapter 2: FUNCTIONS
    Functions, Equivalence relations, Permutations, Review

  • Chapter 3: GROUPS
    Definition of a Group, Subgroups, Constructing Examples, Isomorphisms, Cyclic Groups, Permutation Groups, Homomorphisms, Cosets, Normal Subgroups, and Factor Groups

  • Chapter 4: POLYNOMIALS
    Fields; Roots of Polynomials, Factors, Polynomials with Integer Coefficients, Existence of Roots

    Commutative rings; Integral Domains, Ring Homomorphisms, Ideals and Factor Rings, Quotient Fields

  • Chapter 6: FIELDS
    Algebraic Elements, Finite and Algebraic Extensions, Geometric Constructions, Splitting fields, Finite Fields, Irreducible Polynomials over Finite Fields, Quadratic Reciprocity

    Isomorphism Theorems, Automorphisms, Conjugacy, Groups Acting on Sets, The Sylow Theorems, Finite Abelian Groups, Solvable Groups, Simple Groups

  • Chapter 8: GALOIS THEORY
    The Galois Group of a Polynomial, Multiplicity of Roots, The Fundamental Theorem of Galois Theory, Solvability by Radicals, Cyclotomic Polynomials, Computing Galois Groups

    Principal Ideal Domains, Unique Factorization Domains, Some Diophantine Equations, INDEX

  • Index of Definitions
  • Index of Theorems
  • Read online Abstract Algebra by John A. Beachy and William D. Blair
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