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A first course in abstract algebra 2nd ed

A first course in abstract algebra 2nd ed (4회 대출)

자료유형
단행본
개인저자
Fraleigh, John B.
서명 / 저자사항
A first course in abstract algebra / John B. Fraleigh.
판사항
2nd ed.
발행사항
[Reading, Mass. :   Addison-Wesley Pub. Co. ,   c1976].  
형태사항
xviii, 455 p. : ill. ; 25 cm.
총서사항
Addison-Wesley series in mathematics
ISBN
0201019841
일반주기
Includes index.  
서지주기
Bibliography: p. 407-409.
일반주제명
Algebra, Abstract.
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090 ▼a 512.02 ▼b F812f2
100 1 ▼a Fraleigh, John B. ▼w cn
245 1 2 ▼a A first course in abstract algebra / ▼c John B. Fraleigh.
250 ▼a 2nd ed.
260 ▼a [Reading, Mass. : ▼b Addison-Wesley Pub. Co. , ▼c c1976].
300 ▼a xviii, 455 p. : ▼b ill. ; ▼c 25 cm.
490 0 ▼a Addison-Wesley series in mathematics
500 ▼a Includes index.
504 ▼a Bibliography: p. 407-409.
650 0 ▼a Algebra, Abstract.

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
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No. 7 소장처 세종학술정보원/과학기술실/ 청구기호 512.02 F812f2 등록번호 452008668 도서상태 대출가능 반납예정일 예약 서비스 M
No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 학술정보관(CDL)/B1 국제기구자료실(보존서고)/ 청구기호 512.02 F812f2 등록번호 412342533 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 2 소장처 학술정보관(CDL)/B1 국제기구자료실(보존서고)/ 청구기호 512.02 F812f2 등록번호 412342534 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 3 소장처 학술정보관(CDL)/B1 국제기구자료실(보존서고)/ 청구기호 512.02 F812f2 등록번호 412342535 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 4 소장처 학술정보관(CDL)/B1 국제기구자료실(보존서고)/ 청구기호 512.02 F812f2 등록번호 412342536 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 5 소장처 학술정보관(CDL)/B1 국제기구자료실(보존서고)/ 청구기호 512.02 F812f2 등록번호 412342537 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 6 소장처 학술정보관(CDL)/B1 국제기구자료실(보존서고)/ 청구기호 512.02 F812f2 등록번호 412444502 도서상태 대출가능 반납예정일 예약 서비스 B M
No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 세종학술정보원/과학기술실/ 청구기호 512.02 F812f2 등록번호 452008668 도서상태 대출가능 반납예정일 예약 서비스 M

컨텐츠정보

목차


CONTENTS
 Section 0 A very few Preliminaries
  0.1 The role of definitions = 1
  0.2 Sets = 2
  0.3 Partitions and equivalence relations = 3
PART Ⅰ 1 GROUPS
 Section 1 Binary Operations
  1.1 Motivation = 9
  1.2 Definition and properties = 9
  1.3 Tables = 11
  1.4 Some words of warning = 12
 Section 2 Groups
  2.1 Motivation = 17
  2.2 Definition and elementary properties = 18
  2.3 Finite groups and group tables = 21
 Section 3 Subgroups
  3.1 Notation and terminology = 27
  3.2 Subsets and subgroups = 28
  3.3 Cyclic subgroups = 30
 Section 4 Permutations Ⅰ
  4.1 Functions and permutations = 35
  4.2 Groups of permutations = 38
  4.3 Two important examples = 40
 Section 5 Permutations Ⅱ
  5.1 Cycles and cyclic notation = 45
  5.2 Even and odd permutations = 47
  5.3 The alternating groups = 49
 Section 6 Cyclic Groups
  6.1 Elementary properties = 52
  6.2 The classification of cyclic groups = 54
  6.3 Subgroups of finite cyclic groups = 56
 Section 7 Isomorphism
  7.1 Definition and elementary properties = 59
  7.2 How to show that groups are isonorphic = 60
  7.3 How to show that groups are not isomorphic = 62
  7.4 Cayley's theorem = 63
 Section 8 Direct Products
  8.1 External direct products = 69
  8.2 Internal direct products = 73
 Section 9 Finitely Generated Abelian Groups
  9.1 Generators and torsion = 77
  9.2 The fundamental theorem = 79
  9.3 Applications = 81
 Section 10 Groups in Geometry and Analysis
  10.1 Groups in geometry = 84
  10.2 Groups in analysis = 88
 Section 11 Groups of Cosets
  11.1 Introduction = 92
  11.2 Cosets = 93
  11.3 Applications = 97
 Section 12 Normal Subgroups and Factor Groups
  12.1 Criteria for the existence of a coset group = 101
  12.2 Inner automorphisms and normal subgroups = 102
  12.3 Factor groups = 104
  12.4 Simple groups = 107
  12.5 Applications = 107
 Section 13 Homomorphisms
  13.1 Definition and elementary properties = 112
  13.2 The fundamental homomorphism theorem = 114
  13.3 Applications = 116
  13.4 The first isomorphism theorem = 117
 Section 14 Series of Groups
  14.1 Subnormal and normal scries = 121
  14.2 The Jordan-H$$\ddot o$$lder theorem = 122
  14.3 The center and the .ascending central scries = 125
 Section 15 The Sylow Theorems
  15.1 Conjugate classes and the class equation = 128
  15.2 The Sylow theorems = 129
  15.3 Applications to p-groups = 130
  15.4 Some proofs = 131
 Section 16 Applications of the Sylow Theory
  16.1 More applications to p-groups = 135
  16.2 Further applications = 136
 Section 17 Free Groups
  17.1 Words and reduced words = 140
  17.2 Free groups = 141
  17.3 Homomorphisms of free groups = 142
  17.4 Free abelian groups = 143
 Section 18 Group Presentations
  18.1 Definition = 149
  18.2 Isomorphic presentations = 150
  18.3 Applications = 151
 Section 19 Simplicial Complexes and Homology Groups
  19.1 Motivation = 157
  19.2 Preliminary notions = 158
  19.3 Chains, cycles, and boundaries = 160
  19.4 $$%^2$$ = 0 and homology groups = 163
 Section 20 Computations of Homology Groups
  20.1 Triangulations = 166
  20.2 Invariance properties = 166
  20.3 Connected and contractible spaces = 167
  20.4 Further computations = 169
 Section 21 More Homology Computations and Applications
  21.1 One-sided surfaces = 174
  21.2 The Euler characteristic = 176
  21.3 Mappings of spaces = 178
 Section 22 Homological Algebra
  22.1 Chain complexes and mappings = 183
  22.2 Relative homology = 185
  22.3 The exact homology sequence of a pair = 188
PART Ⅱ I RINGS AND FIELDS
 Section 23 Rings
  23.1 Definition and basic properties = 195
  23.2 Multiplicative questions ; fields = 197
 Section 24 Integral Domains
  24.1 Divisors of zero and cancellation = 202
  24.2 Integral domains = 204
  24.3 The characteristic of a ring = 205
  24.4 Fermat's theorem = 205
  24.5 Euler's generalization = 206
 Section 25 Some Noncommutative Examples
  25.1 Matrices over a field = 209
  25.2 Rings of endomorphisms = 211
  25.3 Group rings and group algebras = 213
  25.4 The quaternions = 215
 Section 26 The Field of Quotients of an Integral Domain
  26.1 The construction = 219
  26.2 Uniqueness = 223
 Section 27 Our Basic Goal = 227
 Section 28 Quotient Rings and Ideals
  28.1 Introduction = 230
  28.2 Criteria for the existence of a coset ring = 231
  28.3 Ideals and quotient rings = 232
 Section 29 Homomorphisms of Rings
  29.1 Definition and elementary properties = 236
  29.2 Maximal and prime ideals = 238
  29.3 Prime fields = 240
 Section 30 Rings of Polynomials
  30.1 Polynomials in an indeterminate = 244
  30.2 The evaluation homomorphisms = 247
  30.3 The new approach = 250
 Section 31 Factorization of Polynomials Over a Field
  31.1 The division algorithm in F[x] = 254
  31.2 Irreducible polynomials = 258
  31.3 Ideal structure in F[x] = 261
  31.4 Uniqueness of factorization in F[x] = 262
 Section 32 Unique Factorization Domains
  32.1 introduction = 266
  32.2 Every PID is UFD = 271
  32.3 If D is a UFD, then D[x] is a UFD = 271
 Section 33 Euclidean Domains
  33.1 Introduction and definition = 278
  33.2 Arithmetic in Euclidean domains = 279
 Section 34 Gaussian Integers and Norms
  34.1 Gaussian integers = 286
  34.2 Muliplicative norms = 288
 Section 35 Introduction to Extension Fields
  35.1 Our basic goal achieved = 293
  35.2 Algebraic and transcendental elements = 295
  35.3 The irreducible polynomial for a over F = 296
  35.4 Simple extensions = 297
 Section 36 Vector Spaces
  36.1 Definition and elementary properties = 302
  36.2 Linear independence and bases = 304
  36.3 Dimension = 305
  36.4 An application to field theory = 307
 Section 37 Further Algebraic Structures
  37.1 Groups with operators = 311
  37.2 Modules = 313
  37.3 Algebras = 314
 Section 38 Algebraic Extensions
  38.1 Finite extensions = 317
  38.2 Algebraically closed fields and algebraic closures = 321
  38.3 The existence of an algebraic closure = 322
 Section 39 Geometric Constructions
  39.1 Constructible numbers = 328
  39.2 The impossibility of certain constructions = 331
 Section 40 Automorphisms of Fields
  40.1 The basic isomorphisms of algebraic field theory = 335
  40.2 Automorphisms and fixed fields = 338
  40.3 The Frobenius automorphism = 341
 Section 41 The Isomorphism Extension Theorem
  41.1 The extension theorem = 345
  41.2 The index of a field extension = 347
  41.3 Proof of the extension theorem = 349
 Section 42 Splitting Fields = 353
 Section 43 Separable Extensions
  43.1 Multiplicity of zeros of a polynomial = 358
  43.2 Separable extensions = 360
  43.3 Perfect fields = 361
  43.4 The primitive element theorem = 363
 Section 44 Totally Inseparable Extensions
  44.1 Totally inseparable extensions = 366
  44.2 Separable closures = 367
 Section 45 Finite Fields
  45.1 The structure of a finite field = 370
  45.2 The existence of GF ($$p^n$$) = 372
 Section 46 Galois Theory
  46.1 R$$\acute e$$sum$$\acute e$$ = 375
  46.2 Normal extensions = 375
  46.3 The main theorem = 377
  46.4 Galois gro %s over finite fields = 379
  46.5 Proof of the %ain theorem completed = 380
 Section 47 Illustrations of Galois Theory
  47 1 Symmetric functions = 385
  47 2 Examples = 387
 Section 48 Cyclotomic Extensions
  48.1 The Galois group of a cyclotomic extension = 393
  48.2 Constructible polygons = 395
 Section 49 Insolvability of the Quintic
  49.1 The problem = 400
  49.2 Extensions by radicals = 400
  49.3 The insolvability of the quintic = 402
Bibliography = 407
Answers and Comments = 411
Notations = 443
Index = 447


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