Solutions Manual to Accompany Introduction to Abstract Algebra, 4e, Solutions Manual

Detalles Bibliográficos
Autor principal: Nicholson, W. Keith
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2012.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • Chapter 0: Preliminaries
  • 0.1 Proofs
  • 0.2 Sets
  • 0.3 Mappings
  • 0.4 Equivalences
  • Chapter 1: Integers and Permutations
  • 1.1 Induction
  • 1.2 Divisors and Prime Factorization
  • 1.3 Integers Modulo n
  • 1.4 Permutations
  • Chapter 2: Groups
  • 2.1 Binary Operations
  • 2.2 Groups
  • 2.3 Subgroups
  • 2.4 Cyclic Groups and the Order of an Element
  • 2.5 Homomorphisms and Isomorphisms
  • 2.6 Cosets and Lagrange's Theorem
  • 2.7 Groups of Motions and Symmetries
  • 2.8 Normal Subgroups
  • 2.9 Factor Groups
  • 2.10 The Isomorphism Theorem
  • 2.11 An Application to Binary Linear Codes
  • Chapter 3: Rings
  • 3.1 Examples and Basic Properties
  • 3.2 Integral Domains and Fields
  • 3.3 Ideals and Factor Rings
  • 3.4 Homomorphisms
  • 3.5 Ordered Integral Domains
  • Chapter 4: Polynomials
  • 4.1 Polynomials
  • 4.2 Factorization of Polynomials over a Field
  • 4.3 Factor Rings of Polynomials over a Field
  • 4.4 Partial Fractions
  • 4.5 Symmetric Polynomials
  • Chapter 5: Factorization in Integral Domains
  • 5.1 Irreducibles and Unique Factorization
  • 5.2 Principal Ideal Domains
  • Chapter 6: Fields
  • 6.1 Vector Spaces
  • 6.2 Algebraic Extensions
  • 6.3 Splitting Fields
  • 6.4 Finite Fields
  • 6.5 Geometric Constructions
  • 6.7 An Application to Cyclic and Bch Codes
  • Chapter 7: Modules over Principal Ideal Domains
  • 7.1 Modules
  • 7.2 Modules over a Principal Ideal Domain
  • Chapter 8: P-groups and the Sylow Theorems
  • 8.1 Products and Factors
  • 8.2 Cauchy's Theorem
  • 8.3 Group Actions
  • 8.4 The Sylow Theorems
  • 8.5 Semidirect Products
  • 8.6 An Application to Combinatorics
  • Chapter 9: Series of Subgroups
  • 9.1 The Jordan-Hölder Theorem
  • 9.2 Solvable Groups
  • 9.3 Nilpotent Groups
  • Chapter 10: Galois Theory
  • 10.1 Galois Groups and Separability
  • 10.2 The Main Theorem of Galois Theory
  • 10.3 Insolvability of Polynomials
  • 10.4 Cyclotomic Polynomials and Wedderburn's Theorem
  • Chapter 11: Finiteness Conditions for Rings and Modules
  • 11.1 Wedderburn's Theorem
  • 11.2 The Wedderburn-artin Theorem
  • Appendices
  • Appendix A: Complex Numbers
  • Appendix B: Matrix Arithmetic
  • Appendix C: Zorn's Lemma

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