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Abstract Algebra 
Foote, Richard M. ¤Ó Wiley
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9780471433347/0471433349
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    Prefacep. xi
    Preliminariesp. 1
    Basicsp. 1
    Properties of the Integersp. 4
    Z / n Z: The Integers Modulo np. 8
    Group Theoryp. 13
    Introduction to Groupsp. 16
    Basic Axioms and Examplesp. 16
    Dihedral Groupsp. 23
    Symmetric Groupsp. 29
    Matrix Groupsp. 34
    The Quaternion Groupp. 36
    Homomorphisms and Isomorphismsp. 36
    Group Actionsp. 41
    Subgroupsp. 46
    Definition and Examplesp. 46
    Centralizers and Normalizers, Stabilizers and Kernelsp. 49
    Cyclic Groups and Cyclic Subgroupsp. 54
    Subgroups Generated by Subsets of a Groupp. 61
    The Lattice of Subgroups of a Groupp. 66
    Quotient Groups and Homomorphismsp. 73
    Definitions and Examplesp. 73
    More on Cosets and Lagrange's Theoremp. 89
    The Isomorphism Theoremsp. 97
    Composition Series and the Holder Programp. 101
    Transpositions and the Alternating Groupp. 106
    Group Actionsp. 112
    Group Actions and Permutation Representationsp. 112
    Groups Acting on Themselves by Left Multiplication--Cayley's Theoremp. 118
    Groups Acting on Themselves by Conjugation--The Class Equationp. 122
    Automorphismsp. 133
    The Sylow Theoremsp. 139
    The Simplicity of A[subscript n]p. 149
    Direct and Semidirect Products and Abelian Groupsp. 152
    Direct Productsp. 152
    The Fundamental Theorem of Finitely Generated Abelian Groupsp. 158
    Table of Groups of Small Orderp. 167
    Recognizing Direct Productsp. 169
    Semidirect Productsp. 175
    Further Topics in Group Theoryp. 188
    p-groups, Nilpotent Groups, and Solvable Groupsp. 188
    Applications in Groups of Medium Orderp. 201
    A Word on Free Groupsp. 215
    Ring Theoryp. 222
    Introduction to Ringsp. 223
    Basic Definitions and Examplesp. 223
    Examples: Polynomial Rings, Matrix Rings, and Group Ringsp. 233
    Ring Homomorphisms an Quotient Ringsp. 239
    Properties of Idealsp. 251
    Rings of Fractionsp. 260
    The Chinese Remainder Theoremp. 265
    Euclidean Domains, Principal Ideal Domains and Unique Factorization Domainsp. 270
    Euclidean Domainsp. 270
    Principal Ideal Domains (P.I.D.s)p. 279
    Unique Factorization Domains (U.F.D.s)p. 283
    Polynomial Ringsp. 295
    Definitions and Basic Propertiesp. 295
    Polynomial Rings over Fields Ip. 299
    Polynomial Rings that are Unique Factorization Domainsp. 303
    Irreducibility Criteriap. 307
    Polynomial Rings over Fields IIp. 313
    Polynomials in Several Variables over a Field and Grobner Basesp. 315
    Modules and Vector Spacesp. 336
    Introduction to Module Theoryp. 337
    Basic Definitions and Examplesp. 337
    Quotient Modules and Module Homomorphismsp. 345
    Generation of Modules, Direct Sums, and Free Modulesp. 351
    Tensor Products of Modulesp. 359
    Exact Sequences--Projective, Injective, and Flat Modulesp. 378
    Vector Spacesp. 408
    Definitions and Basic Theoryp. 408
    The Matrix of a Linear Transformationp. 415
    Dual Vector Spacesp. 431
    Determinantsp. 435
    Tensor Algebras, Symmetric and Exterior Algebrasp. 441
    Modules over Principal Ideal Domainsp. 456
    The Basic Theoryp. 458
    The Rational Canonical Formp. 472
    The Jordan Canonical Formp. 491
    Field Theory and Galois Theoryp. 509
    Field Theoryp. 510
    Basic Theory of Field Extensionsp. 510
    Algebraic Extensionsp. 520
    Classical Straightedge and Compass Constructionsp. 531
    Splitting Fields and Algebraic Closuresp. 536
    Separable and Inseparable Extensionsp. 545
    Cyclotomic Polynomials and Extensionsp. 552
    Galois Theoryp. 558
    Basic Definitionsp. 558
    The Fundamental Theorem of Galois Theoryp. 567
    Finite Fieldsp. 585
    Composite Extensions and Simple Extensionsp. 591
    Cyclotomic Extensions and Abelian Extensions over Qp. 596
    Galois Groups of Polynomialsp. 606
    Solvable and Radical Extensions: Insolvability of the Quinticp. 625
    Computation of Galois Groups over Qp. 640
    Transcendental Extensions, Inseparable Extensions, Infinite Galois Groupsp. 645
    An Introduction to Commutative Rings, Algebraic Geometry, and Homological Algebrap. 655
    Commutative Rings and Algebraic Geometryp. 656
    Noetherian Rings and Affine Algebraic Setsp. 656
    Radicals and Affine Varietiesp. 673
    Integral Extensions and Hilbert's Nullstellensatzp. 691
    Localizationp. 706
    The Prime Spectrum of a Ringp. 731
    Artinian Rings, Discrete Valuation Rings, and Dedekind Domainsp. 750
    Artinian Ringsp. 750
    Discrete Valuation Ringsp. 755
    Dedekind Domainsp. 764
    Introduction to Homological Algebra and Group Cohomologyp. 776
    Introduction to Homological Algebra--Ext and Torp. 777
    The Cohomology of Groupsp. 798
    Crossed Homomorphisms and H[superscript 1](G, A)p. 814
    Group Extensions, Factor Sets and H[superscript 2](G, A)p. 824
    Introduction to the Representation Theory of Finite Groupsp. 839
    Representation Theory and Character Theoryp. 840
    Linear Actions and Modules over Group Ringsp. 840
    Wedderburn's Theorem and Some Consequencesp. 854
    Character Theory and the Orthogonality Relationsp. 864
    Examples and Applications of Character Theoryp. 880
    Characters of Groups of Small Orderp. 880
    Theorems of Burnside and Hallp. 886
    Introduction to the Theory of Induced Charactersp. 892
    Cartesian Products and Zorn's Lemmap. 905
    Category Theoryp. 911
    Indexp. 919
    Table of Contents provided by Rittenhouse. All Rights Reserved.
  • Foote, Richard M. [Àú]
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