Introduction to Abstract Algebra, Solutions Manual, 4th Edition

Contents

Cover

Title Page

Copyright

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 Modulon

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