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Abstract algebra 3rd ed

Abstract algebra 3rd ed (32회 대출)

자료유형
단행본
개인저자
Dummit, David Steven. Foote, Richard M., 1950-.
서명 / 저자사항
Abstract algebra / David S. Dummit, Richard M. Foote.
판사항
3rd ed.
발행사항
Hoboken, NJ :   Wiley,   c2004.  
형태사항
xii, 932 p. : ill. ; 25 cm.
ISBN
9780471433347 0471433349 (acid-free paper)
일반주기
Includes index.  
일반주제명
Algebra, Abstract.
000 00849camuu2200289 a 4500
001 000045741927
005 20130307172646
008 130307s2004 njua 001 0 eng
010 ▼a 2003057652
020 ▼a 9780471433347
020 ▼a 0471433349 (acid-free paper)
035 ▼a (KERIS)REF000009487105
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA162 ▼b .D85 2004
082 0 4 ▼a 512/.02 ▼2 23
084 ▼a 512.02 ▼2 DDCK
090 ▼a 512.02 ▼b D889a3
100 1 ▼a Dummit, David Steven.
245 1 0 ▼a Abstract algebra / ▼c David S. Dummit, Richard M. Foote.
250 ▼a 3rd ed.
260 ▼a Hoboken, NJ : ▼b Wiley, ▼c c2004.
300 ▼a xii, 932 p. : ▼b ill. ; ▼c 25 cm.
500 ▼a Includes index.
650 0 ▼a Algebra, Abstract.
700 1 ▼a Foote, Richard M., ▼d 1950-.
945 ▼a KLPA

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.02 D889a3 등록번호 121223783 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 2 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.02 D889a3 등록번호 121247371 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차


CONTENTS
Preface = xi
Preliminaries = 1
 0.1 Basics = 1
 0.2 Properties of the Integers = 4
 0.3 Z/n Z : The Integers Modulo n = 8
Part Ⅰ - GROUP THEORY = 13
 Chapter 1 Introduction to Groups = 16
  1.1 Basic Axioms and Examples = 16
  1.2 Dihedral Groups = 23
  1.3 Symmetric Groups = 29
  1.4 Matrix Groups = 34
  1.5 The Quaternion Group = 36
  1.6 Homomorphisms and Isomorphisms = 36
  1.7 Group Actions = 41
 Chapter 2 Subgroups = 46
  2.1 Definition and Examples = 46
  2.2 Centralizers and Normalizers, Stabilizers and Kernels = 49
  2.3 Cyclic Groups and Cyclic Subgroups = 54
  2.4 Subgroups Generated by Subsets of a Group = 61
  2.5 The Lattice of Subgroups of a Group = 66
 Chapter 3 Quotient Groups and Homomorphisms = 73
  3.1 Definitions and Examples = 73
  3.2 More on Cosets and Lagrange's Theorem = 89
  3.3 The Isomorphism Theorems = 97
  3.4 Composition Series and the H$$\ddot o$$lder Program = 101
  3.5 Transpositions and the Alternating Group = 106
 Chapter 4 Group Actions = 112
  4.1 Group Actions and Permutation Representations = 112
  4.2 Groups Acting on Themselves by Left Multiplication - Cayley's Theorem = 118
  4.3 Groups Acting on Themselves by Conjugation - The Class Equation = 122
  4.4 Automorphisms = 133
  4.5 The Sylow Theorems = 139
  4.6 The Simplicity of $$A_n$$ = 149
 Chapter 5 Direct and Semidirect Products and Abelian Groups = 152
  5.1 Direct Products = 152
  5.2 The Fundamental Theorem of Finitely Generated Abelian Groups = 158
  5.3 Table of Groups of Small Order = 167
  5.4 Recognizing Direct Products = 169
  5.5 Semidirect Products = 175
 Chapter 6 Further Topics in Group Theory = 188
  6.1 p-groups, Nilpotent Groups, and Solvable Groups = 188
  6.2 Applications in Groups of Medium Order = 201
  6.3 A Word on Free Groups = 215
Part Ⅱ - RING THEORY = 222
 Chapter 7 Introduction to Rings = 223
  7.1 Basic Definitions and Examples = 223
  7.2 Examples : Polynomial Rings, Matrix Rings, and Group Rings = 233
  7.3 Ring Homomorphisms an Quotient Rings = 239
  7.4 Properties of Ideals = 251
  7.5 Rings of Fractions = 260
  7.6 The Chinese Remainder Theorem = 265
 Chapter 8 Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains = 270
  8.1 Euclidean Domains = 270
  8.2 Principal Ideal Domains(P.I.D.s) = 279
  8.3 Unique Factorization Domains(U.F.D.s) = 283
 Chapter 9 Polynomial Rings = 295
  9.1 Definitions and Basic Properties = 295
  9.2 Polynomial Rings over Fields Ⅰ = 299
  9.3 Polynomial Rings that are Unique Factorization Domains = 303
  9.4 Irreducibility Criteria = 307
  9.5 Polynomial Rings over Fields Ⅱ = 313
  9.6 Polynomials in Several Variables over a Field and Gr$$\ddot o$$bner Bases = 315
Part Ⅲ - MODULES AND VECTOR SPACES = 336
 Chapter 10 Introduction to Module Theory = 337
  10.1 Basic Definitions and Examples = 337
  10.2 Quotient Modules and Module Homomorphisms = 345
  10.3 Generation of Modules, Direct Sums, and Free Modules = 351
  10.4 Tensor Products of Modules = 359
  10.5 Exact Sequences - Projective, Injective, and Flat Modules = 378
 Chapter 11 Vector Spaces = 408
  11.1 Definitions and Basic Theory = 408
  11.2 The Matrix of a Linear Transformation = 415
  11.3 Dual Vector Spaces = 431
  11.4 Determinants = 435
  11.5 Tensor Algebras, Symmetric and Exterior Algebras = 441
 Chapter 12 Modules over Principal Ideal Domains = 456
  12.1 The Basic Theory = 458
  12.2 The Rational Canonical Form = 472
  12.3 The Jordan Canonical Form = 491
Part Ⅳ - FIELD THEORY AND GALOIS THEORY = 509
 Chapter 13 Field Theory = 510
  13.1 Basic Theory of Field Extensions = 510
  13.2 Algebraic Extensions = 520
  13.3 Classical Straightedge and Compass Constructions = 531
  13.4 Splitting Fields and Algebraic Closures = 536
  13.5 Separable and Inseparable Extensions = 545
  13.6 Cyclotomic Polynomials and Extensions = 552
 Chapter 14 Galois Theory = 558
  14.1 Basic Definitions = 558
  14.2 The Fundamental Theorem of Galois Theory = 567
  14.3 Finite Fields = 585
  14.4 Composite Extensions and Simple Extensions = 591
  14.5 Cyclotomic Extensions and Abelian Extensions over Q = 596
  14.6 Galois Groups of Polynomials = 606
  14.7 Solvable and Radical Extensions : Insolvability of the Quintic = 625
  14.8 Computation of Galois Groups over Q = 640
  14.9 Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups = 645
Part Ⅴ - AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA = 655
 Chapter 15 Commutative Rings and Algebraic Geometry = 656
  15.1 Noetherian Rings and Affine Algebraic Sets = 656
  15.2 Radicals and Affine Varieties = 673
  15.3 Integral Extensions and Hilbert's Nullstellensatz = 691
  15.4 Localization = 706
  15.5 The Prime Spectrum of a Ring = 731
 Chapter 16 Artinian Rings, Discrete Valuation Rings, and Dedekind Domains = 750
  16.1 Artinian Rings = 750
  16.2 Discrete Valuation Rings = 755
  16.3 Dedekind Domains = 764
 Chapter 17 Introduction to Homological Algebra and Group Cohomology = 776
  17.1 Introduction to Homological Algebra-Ext and Tor = 777
  17.2 The Cohomology of Groups = 798
  17.3 Crossed Homomorphisms and H¹(G, A) = 814
  17.4 Group Extensions, Factor Sets and H²(G, A) = 824
Part Ⅵ - INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS = 839
 Chapter 18 Representation Theory and Character Theory = 840
  18.1 Linear Actions and Modules over Group Rings = 840
  18.2 Wedderburn's Theorem and Some Consequences = 854
  18.3 Character Theory and the Orthogonality Relations = 864
 Chapter 19 Examples and Applications of Character Theory = 880
  19.1 Characters of Groups of Small Order = 880
  19.2 Theorems of Burnside and Hall = 886
  19.3 Introduction to the Theory of Induced Characters = 892
Appendix Ⅰ : Cartesian Products and Zorn's Lemma = 905
Appendix Ⅱ : Category Theory = 911
Index = 919


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