Abstract algebra
By: David S. Dummit, Richard M. Foote.
Contributors: Foote, Richard M., 1950-
Edition: 3rd ed.
Publisher: Wiley
Published: 2004
Place of publication: Hoboken, NJ
Language: eng
Format: Hardcover
Number of pages: 932
Subjects: Algebra, Abstract.
Notes: Includes index.
Table of contents: title: Preface
pagenum: xi; title: Preliminaries
pagenum: 1; label: 0.1
title: Basics
pagenum: 1; label: 0.2
title: Properties of the Integers; label: 0.3
title: Z/nZ: The Integers Modulo n
pagenum: 8; label: Part I
title: Group Theory
pagenum: 13; label: 1
title: Introduction to Groups
pagenum: 16; label: 1.1
title: Basic Axioms and Examples
pagenum: 16; label: 1.2
title: Dihedral Groups
pagenum: 23; label: 1.3
title: Symmetric Groups
pagenum: 29; label: 1.4
title: Matrix Groups
pagenum: 34; label: 1.5
title: The Quaternion Group
pagenum: 36; label: 1.6
title: Homomorphisms and Isomorphisms
pagenum: 36; label: 1.7
title: Group Actions
pagenum: 41; label: 2
title: Subgroups
pagenum: 46; label: 2.1
title: Definitions and Examples
pagenum: 46; label: 2.2
title: Centralizers and Normalizers, Stabilizers and Kernels
pagenum: 49; label: 2.3
title: Cyclic Groups and Cyclic Subgroups
pagenum: 54; label: 2.4
title: Subgroups Generated by Subsets of a Group
pagenum: 61; label: 2.5
title: The Lattice of Subgroups of a Group
pagenum: 66; label: 3
title: Quotient Groups and Homomorphisms
pagenum: 73; label: 3.1
title: Definitions and Examples
pagenum: 73; label: 3.2
title: More on Cosets and Lagrange's Theorem
pagenum: 89; label: 3.3
title: The Isomorphism Theorems
pagenum: 97; label: 3.4
title: Composition Series and the Holder Program
pagenum: 101; label: 3.5
title: Transpositions and the Alternating Group
pagenum: 106; label: 4
title: Group Actions
pagenum: 112; label: 4.1
title: Group Actions and Permutation Representations
pagenum: 112; label: 4.2
title: Groups Acting on Themselves by Left Multiplication-Cayley's Theorem
pagenum: 118; label: 4.3
title: Groups Acting on Themselves by Conjugation-The Class Equation
pagenum: 122; label: 4.4
title: Automorphism
pagenum: 133; label: 4.5
title: The Sylow Theorems
pagenum: 139; label: 4.6
title: The Simplicity of An
pagenum: 149; label: 5
title: Direct and Semidirect Products and Abelian Groups
pagenum: 152; label: 5.1
title: Direct Products
pagenum: 142; label: 5.2
title: The Fundamental Theorem of Finitely Generated Ableian Groups
pagenum: 158; label: 5.3
title: Table of Groups of Small Order
pagenum: 167; label: 5.4
title: Recognizing Direct Products
pagenum: 169; label: 5.5
title: Semidirect Products
pagenum: 175; label: 6
title: Further Topics in Group Theory
pagenum: 188; label: 6.1
title: p-groups, Nilpotent Groups, and Solvable Groups
pagenum: 188; label: 6.2
title: Applications in Groups of Medium Order
pagenum: 201; label: 6.3
title: A Word on Free Groups
pagenum: 215; label: Part II
title: Ring Theory
pagenum: 222; label: 7
title: Introduction to Rings
pagenum: 223; label: 7.1
title: Basic Definitions and Exmaples
pagenum: 223; label: 7.2
title: Examples: Polynomial Rings, Matri Rings, and Group Rings
pagenum: 233; label: 7.3
title: Ring Homomorphisms and Quotinet Rings
pagenum: 239; label: 7.4
title: Properties of Ideals
pagenum: 251; label: 7.5
title: Rings of fractions
pagenum: 260; label: 7.6
title: The Chinese Remainder Theorem
pagenum: 265; label: 8
title: Euclidean Domains, Principla Ideal Domains and Unique Factorization Domains
pagenum: 270; label: 8.1
title: Euclidean Domains
pagenum: 270; label: 8.2
title: Principal Ideal Domains (P.I.D.s)
pagenum: 279; label: 8.3
title: Unique Factorization Domains (U.F.D.s)
pagenum: 283; label: 9
title: Polynomial Rings
pagenum: 295; label: 9.1
title: Definitions and Basic Properties
pagenum: 295; label: 9.2
title: Polynomial Rings over Fields I
pagenum: 299; label: 9.3
title: Polynomial Rings that are Unique Factorization Domains
pagenum: 303; label: 9.4
title: Irreducibility Criteria
pagenum: 307; label: 9.5
title: Polynomial rings over Fields II
pagenum: 313; label: 9.6
title: Polynomials in Several Variables over a Field and Grobner Bases
pagenum: 315; label: Part III
title: Modules and Vector Spaces
pagenum: 336; label: 10
title: Introduction to Module Theory
pagenum: 337; label: 10.1
title: Basic Definitions and Examples
pagenum: 337; label: 10.2
title: Quotient Modules and Module Homomorphisms
pagenum: 345; label: 10.3
title: Generation of Modules, Direct Sums, and Free Modules
pagenum: 351; label: 10.4
title: Tensor Product of Modules
pagenum: 359; label: 10.5
title: Exact Sequences - Projective, Injective, and Flat Modules
pagenum: 378; label: 11
title: vector Spaces
pagenum: 408; label: 11.1
title: Definitions and Basic Theory
pagenum: 408; label: 11.2
title: The Matrix of a Linear Transformation
pagenum: 415; label: 11.3
title: Dual Vector Spaces
pagenum: 431; label: 11.4
title: Determinants
pagenum: 435; label: 11.5
title: Tensor Algebras, Symmetric and Exterior Algebras
pagenum: 441; label: 12
title: Modules over Principal Ideal Domains
pagenum: 456; label: 12.1
title: The Basic Theory
pagenum: 458; label: 12.2
title: The Rational Canonical From
pagenum: 472; label: 12.3
title: The Jordan Canonical From
pagenum: 491; label: 13
title: Field Theory
pagenum: 510; label: 13.1
title: Basic Theory of field Extensions
pagenum: 510; label: 13.2
title: Algebraic extensions
pagenum: 520; label: 13.3
title: Classical Straightedge and Compass Constructions
pagenum: 531; label: 13.4
title: Splitting Fields and Algebraic Closures
pagenum: 536; label: 13.5
title: Separable and Inseparable Extensions
pagenum: 545; label: 13.6
title: Cyclotomic Polynomials and Extensions
pagenum: 552; label: 14
title: Galios Theory
pagenum: 558; label: 14.1
title: Basic Definitions
pagenum: 558; label: 14.2
title: The Fundamental Theorem of Galios Theory
pagenum: 567; label: 14.3
title: Finite Fields
pagenum: 585; label: 14.4
title: Composite Extensions and Simple Extensions
pagenum: 591; label: 14.5
title: Cyclotomic Extensions and Albelian Extensions over Q
pagenum: 596; label: 14.6
title: Galois Groups of Polynomials
pagenum: 606; label: 14.7
title: Solvable and Radical Extensions: Insolvability of the Quintic
pagenum: 625; label: 14.8
title: Computation of the Galois Groups over Q
pagenum: 640; label: 14.9
title: Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups
pagenum: 645; label: Part V [sic]
title: An Introduction to Comutative Rings, Algebraic Geometry, and Homological Algebra
pagenum: 655; label: 15
title: Commutative Rings and Algebraic Geometry
pagenum: 656; label: 15.1
title: Noetherian Rings and Affine Algebraic Sets
pagenum: 656; label: 15.2
title: Radicals and Affine Varieties
pagenum: 673; label: 15.3
title: Integral Extensions and Hilbert's Nullstellensatz
pagenum: 691; label: 15.4
title: Localization
pagenum: 706; label: 15.5
title: The Prime Spectrum of a Ring
pagenum: 731; label: 16
title: Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
pagenum: 750; label: 16.1
title: Artinian Rings
pagenum: 750; label: 16.2
title: Discrete Valuation Rings
pagenum: 755; label: 16.3
title: Dedekind Domains
pagenum: 764; label: 17
title: Introduction to Homological Algebra and Group Cohomology
pagenum: 776; label: 17.1
title: Introduction to Homological Algebra - Ext and Tor
pagenum: 777; label: 17.2
title: The Cohomology of Groups
pagenum: 798; label: 17.3
title: Crossed Homomorphisms and H1(G, A)
pagenum: 814; label: 17.4
title: Group Extensions, Factor Sets and H2(G, A)
pagenum: 824; label: Part VI
title: Introduction to the Representation Theory of Finite Groups
pagenum: 839; label: 18
title: Representation Theory and Character Theory
pagenum: 840; label: 18.1
title: Linear Actions and Modules over Group Rings
pagenum: 840; label: 18.2
title: Wedderburn's Theorem and Some Consequences
pagenum: 854; label: 18.3
title: Character Theory and the Orthogonality Relations
pagenum: 864; label: 19
title: Examples and Applications of Character Theory
pagenum: 880; label: 19.1
title: Characters of Groups of Small Order
pagenum: 880; label: 19.2
title: Theorems of Burnside and Hall
pagenum: 886; label: 19.3
title: Introduction to the Theory of Induced Characters
pagenum: 892; label: Appendix I
title: Cartesian Products and Zorn's Lemma
pagenum: 905; label: Appendix II
title: Category Theory
pagenum: 911; title: Index
pagenum: 919