- #1
- 22,183
- 3,322
- Author: Thomas Hungerford
- Title: Algebra
- Amazon link: https://www.amazon.com/dp/0387905189/?tag=pfamazon01-20
Table of Contents:
Code:
[LIST]
[*] Preface
[*] Acknowledgments
[*] Suggestions on the Use of This Book
[*] Introduction: Prerequisites and Preliminaries
[LIST]
[*] Logic
[*] Sets and Classes
[*] Functions
[*] Relations and Partitions
[*] Products
[*] The Integers
[*] The Axiom of Choice, Order and Zorn's Lemma
[*] Cardinal Numbers
[/LIST]
[*] Groups
[LIST]
[*] Semigroups, Monoids and Groups
[*] Homomorphisms and Subgroups
[*] Cyclic Groups
[*] Cosets and Counting
[*] Normality, Quotient Groups, and Homomorphisms
[*] Symmetric, Alternating, and Dihedral Groups
[*] Categories: Products, Coproducts, and Free Objects
[*] Direct Products and Direct Sums
[*] Free Groups, Free Products, Generators & Relations
[/LIST]
[*] The Structure of Groups
[LIST]
[*] Free Abelian Groups
[*] Finitely Generated Abelian Groups
[*] The Krull-Schmidt Theorem
[*] The Action of a Group on a Set
[*] The Sylow Theorems
[*] Classification of Finite Groups
[*] Nilpotent and Solvable Groups
[*] Normal and Subnormal Series
[/LIST]
[*] Rings
[LIST]
[*] Rings and Homomorphisms
[*] Ideals
[*] Factorization in Commutative Rings
[*] Rings of Quotients and Localization
[*] Rings of Polynomials and Formal Power Series
[*] Factorization in Polynomial Rings
[/LIST]
[*] Modules
[LIST]
[*] Modules, Homomorphisms and Exact Sequences
[*] Free Modules and Vector Spaces
[*] Projective and Injective Modules
[*] Hom and Duality
[*] Tensor Products
[*] Modules over a Principal Ideal Domain
[*] Algebras
[/LIST]
[*] Fields and Galois Theory
[LIST]
[*] Field Extensions
[*] Appendix: Ruler and Compass Constructions
[*] The Fundamental Theorem
[*] Appendix: Symmetric Rational Functions
[*] Splitting Fields, Algebraic Closure and Normality
[*] Appendix: The Fundamental Theorem of Algebra
[*] The Galois Group of a Polynomial
[*] Finite Fields
[*] Separability
[*] Cyclic Extensions
[*] Cyclotomic Extensions
[*] Radical Extensions
[*] Appendix: The General Equation of Degree n
[/LIST]
[*] The Structure of Fields
[LIST]
[*] Transcendence Bases
[*] Linear Disjointness and Separability
[/LIST]
[*] Linear Algebra
[LIST]
[*] Matrices and Maps
[*] Rank and Equivalence
[*] Appendix: Abelian Groups Defined by Generators and Relations
[*] Determinants
[*] Decomposition of a Single Linear Transformation and Similarity.
[*] The Characteristic Polynomial, Eigenvectors and Eigenvalues
[/LIST]
[*] Commutative Rings and Modules
[LIST]
[*] Chain Conditions
[*] Prime and Primary Ideals
[*] Primary Decomposition
[*] Noetherian Rings and Modules
[*] Ring Extensions
[*] Dedekind Domains
[*] The Hilbert Nullstellensatz
[/LIST]
[*] The Structure of Rings
[LIST]
[*] Simple and Primitive Rings
[*] The Jacobson Radical
[*] Semisimple Rings
[*] The Prime Radical; Prime and Semiprime Rings
[*] Algebras
[*] Division Algebras
[/LIST]
[*] Categories
[LIST]
[*] Functors and Natural Transformations
[*] Adjoint Functors
[*] Morphisms
[/LIST]
[*] List of Symbols
[*] Bibliography
[*] Index
[/LIST]
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