Book:Thomas W. Hungerford/Algebra
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Thomas W. Hungerford: Algebra
Published $\text {1974}$, Springer-Verlag New York, Inc.
- ISBN 0-387-90518-9
Subject Matter
Contents
- Preface
- Acknowledgements
- Suggestions on the Use of This Book
- Introduction: Prerequisites and Preliminaries
- Chapter $\text {I}$: Groups
- 1. Semigroups, Monoids and Groups
- 2. Homomorphisms and Subgroups
- 3. Cyclic Groups
- 4. Cosets and Counting
- 5. Normality, Quotient Groups, and Homomorphisms
- 6. Symmetric, Alternating, and Dihedral Groups
- 7. Categories: Products, Coproducts, and Free Objects
- 8. Direct Products and Direct Sums
- 9. Free Groups, Free Products, Generators & Relations
- Chapter $\text {II}$: The Structure of Groups
- 1. Free Abelian Groups
- 2. Finitely Generated Abelian Groups
- 3. The Krull-Schmidt Theorem
- 4. The Action of a Group on a Set
- 5. The Sylow Theorems
- 6. Classifications of Finite Groups
- 7. Nilpotent and Solvable Groups
- 8. Normal and Subnormal Series
- Chapter $\text {III}$: Rings
- 1. Rings and Homomorphisms
- 2. Ideals
- 3. Factorization in Commutative Rings
- 4. Rings of Quotients and Localization
- 5. Rings of Polynomials and Formal Power Series
- 6. Factorization in Polynomial Rings
- Chapter $\text {IV}$: Modules
- 1. Modules, Homomorphisms and Exact Sequences
- 2. Free Modules and Vector Spaces
- 3. Projective and Injective Modules
- 4. Hom and Duality
- 5. Tensor Products
- 6. Modules over a Principal Ideal Domain
- 7. Algebras
- Chapter $\text {V}$: Fields and Galois Theory
- 1. Field Extensions
- Appendix: Ruler and Compass Construction
- 2. The Fundamental Theorem
- Appendix: Symmetric Rational Functions
- 3. Splitting Fields
- Appendix: The Fundamental Theorem of Algebra
- 4. The Galois Group of a Polynomial
- 5. Finite Fields
- 6. Separability
- 7. Cyclic Extensions
- 8. Cyclotomic Extensions
- 9. Radical Extensions
- Appendix: The General Equation of Degree n
- 1. Field Extensions
- Chapter $\text {VI}$: The Structure of Fields
- 1. Transcendence Bases
- 2. Linear Disjointness and Separability
- Chapter $\text {VII}$: Linear Algebra
- 1. Matrices and Maps
- 2. Rank and Equivalence
- Appendix: Abelian Groups Defined by Generators and Relations
- 3. Determinants
- 4. Decomposition of a Single Linear Transformation and Similarity
- 5. The Characteristic Polynomial, Eigenvectors and Eigenvalues
- Chapter $\text {VIII}$: Commutative Rings and Modules
- 1. Chain Conditions
- 2. Prime and Primary Ideals
- 3. Primary Decomposition
- 4. Noetherian Rings and Modules
- 5. Ring Extensions
- 6. Dedekind Domains
- 7. The Hilbert Nullstellensatz
- Chapter $\text {IX}$: The Structure of Rings
- 1. Simple and Primitive Rings
- 2. The Jacobson Radical
- 3. Semisimple Rings
- 4. The Prime Radical; Prime and Semiprime Rings
- 5. Algebras
- 6. Division Algebras
- Chapter $\text {X}$: Categories
- 1. Functors and Natural Transformations
- 2. Adjoint Functors
- 3. Morphisms
- List of Symbols
- Bibliography
- Index