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Introduction to Abstract Algebra (2nd Edition) by Smith Jonathan D. H



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Introduction to Abstract Algebra (2nd Edition) written by Smith Jonathan D. H. , Iowa State University, Ames, Iowa, USA.

Introduction to Abstract Algebra (2nd Edition) written by Smith Jonathan D. H. cover the following topics.

  • 1. NUMBERS
    1.1 Ordering numbers
    1.2 The Well-Ordering Principle
    1.3 Divisibility
    1.4 The Division Algorithm
    1.5 Greatest common divisors
    1.6 The Euclidean Algorithm
    1.7 Primes and irreducibles
    1.8 The Fundamental Theorem of Arithmetic
    1.9 Exercises
    1.10 Study projects
    1.11 Notes

  • 2. FUNCTIONS
    2.1 Specifying functions
    2.2 Composite functions
    2.3 Linear functions
    2.4 Semigroups of functions
    2.5 Injectivity and surjectivity
    2.6 Isomorphisms
    2.7 Groups of permutations
    2.8 Exercises
    2.9 Study projects
    2.10 Notes
    2.11 Summary

  • 3. EQUIVALENCE
    3.1 Kernel and equivalence relations
    3.2 Equivalence classes
    3.3 Rational numbers
    3.4 The First Isomorphism Theorem for Sets
    3.5 Modular arithmetic
    3.6 Exercises
    3.7 Study projects
    3.8 Notes

  • 4. GROUPS AND MONOIDS
    4.1 Semigroups
    4.2 Monoids
    4.3 Groups
    4.4 Componentwise structure
    4.5 Powers
    4.6 Submonoids and subgroups
    4.7 Cosets
    4.8 Multiplication tables
    4.9 Exercises
    4.10 Study projects
    4.11 Notes

  • 5. HOMOMORPHISMS
    5.1 Homomorphisms
    5.2 Normal subgroups
    5.3 Quotients
    5.4 The First Isomorphism Theorem for Groups
    5.5 The Law of Exponents
    5.6 Cayley’s Theorem
    5.7 Exercises
    5.8 Study projects
    5.9 Notes

  • 6. RINGS
    6.1 Rings
    6.2 Distributivity
    6.3 Subrings
    6.4 Ring homomorphisms
    6.5 Ideals
    6.6 Quotient rings
    6.7 Polynomial rings
    6.8 Substitution
    6.9 Exercises
    6.10 Study projects
    6.11 Notes

  • 7. FIELDS
    7.1 Integral domains
    7.2 Degrees
    7.3 Fields
    7.4 Polynomials over fields
    7.5 Principal ideal domains
    7.6 Irreducible polynomials
    7.7 Lagrange interpolation
    7.8 Fields of fractions
    7.9 Exercises
    7.10 Study projects
    7.11 Notes

  • 8. FACTORIZATION
    8.1 Factorization in integral domains
    8.2 Noetherian domains
    8.3 Unique factorization domains
    8.4 Roots of polynomials
    8.5 Splitting fields
    8.6 Uniqueness of splitting fields
    8.7 Structure of finite fields
    8.8 Galois fields
    8.9 Exercises
    8.10 Study projects
    8.11 Notes

  • 9. MODULES
    9.1 Endomorphisms
    9.2 Representing a ring
    9.3 Modules
    9.4 Submodules
    9.5 Direct sums
    9.6 Free modules
    9.7 Vector spaces
    9.8 Abelian groups
    9.9 Exercises
    9.10 Study projects
    9.11 Notes

  • 10. GROUP ACTIONS
    10.1 Actions
    10.2 Orbits
    10.3 Transitive actions
    10.4 Fixed points
    10.5 Faithful actions
    10.6 Cores
    10.7 Alternating groups
    10.8 Sylow Theorems
    10.9 Exercises
    10.10 Study projects
    10.11 Notes

  • 11. QUASIGROUPS
    11.1 Quasigroups
    11.2 Latin squares
    11.3 Division
    11.4 Quasigroup homomorphisms
    11.5 Quasigroup homotopies
    11.6 Principal isotopy
    11.7 Loops
    11.8 Exercises
    11.9 Study projects
    11.10 Notes

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