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

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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

  • Chapter 5: COMMUTATIVE RINGS
    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

  • Chapter 7: STRUCTURE OF GROUPS
    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

  • Chapter 9: UNIQUE FACTORIZATION
    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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