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Field theory

Field theory (2회 대출)

자료유형
단행본
개인저자
Roman, Steven.
서명 / 저자사항
Field theory / Steven Roman.
발행사항
New York :   Springer-Verlag,   c1995.  
형태사항
xii, 272 p. : ill. ; 24 cm.
총서사항
Graduate texts in mathematics ;158
ISBN
0387944079 (New York : hard : acid-free paper) 0387944087 (New York : soft : acid-free paper)
서지주기
Includes bibliographical references (p. [265]-266) and indexes.
일반주제명
Algebraic fields. Galois theory. Polynomials. Corps alg?briques. Galois, th?orie de. Polyn?mes.
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001 000000424612
005 19961218140619.0
008 940916s1995 nyua b 001 0 eng
010 ▼a 94036400
020 ▼a 0387944079 (New York : hard : acid-free paper)
020 ▼a 0387944087 (New York : soft : acid-free paper)
040 ▼a DLC ▼c DLC ▼d FPU
049 ▼l 111066500
050 0 0 ▼a QA247 ▼b .R598 1995
082 0 0 ▼a 512/.3 ▼2 20
090 ▼a 512.3 ▼b R758f
100 1 ▼a Roman, Steven.
245 1 0 ▼a Field theory / ▼c Steven Roman.
260 ▼a New York : ▼b Springer-Verlag, ▼c c1995.
300 ▼a xii, 272 p. : ▼b ill. ; ▼c 24 cm.
440 0 ▼a Graduate texts in mathematics ; ▼v 158
504 ▼a Includes bibliographical references (p. [265]-266) and indexes.
650 0 ▼a Algebraic fields.
650 0 ▼a Galois theory.
650 0 ▼a Polynomials.
650 7 ▼a Corps alg?briques. ▼2 ram
650 7 ▼a Galois, th?orie de. ▼2 ram
650 7 ▼a Polyn?mes. ▼2 ram

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고7층/ 청구기호 512.3 R758f 등록번호 111066500 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

CONTENTS
Preface = ⅶ
Chapter 0 Preliminaries = 1
  0.1 Lattices = 1
  0.2 Groups = 3
  0.3 Rings = 12
  0.4 Integral Domains = 15
  0.5 Unique Factorization Domains = 17
  0.6 Principal Ideal Domains = 17
  0.7 Euclidean Domains = 18
  0.8 Tensor Products = 19
Part 1 Basic Theory = 23
  Chapter 1 Polynomials = 25
    1.1 Polynomials Over a Ring = 25
    1.2 Primitive Polynomials = 26
    1.3 The Division Algorithm = 28
    1.4 Splitting Fields = 31
    1.5 The Minimal Polynomial = 32
    1.6 Multiple Roots = 33
    1.7 Testing for Irreducibility = 35
  Chapter 2 Field Extensions = 39
    2.1 The Lattice of Subfields of Field = 39
    2.2 Distinguished Extensions = 40
    2.3 Finitely Generated Extensions = 41
    2.4 Simple Extensions = 42
    2.5 Finite Extensions = 43
    2.6 Algebraic Extensions = 45
    2.7 Algebraic Closures = 46
    2.8 Embeddings = 48
    2.9 Splitting Fields and Normal Extensions = 52
  Chapter 3 Algebraic Independence = 61
    3.1 Dependence Relations = 61
    3.2 Algebraic Dependence = 64
    3.3 Transcendence Bases = 67
    3.4 Simple Transcendental Extensions = 73
  Chapter 4 Separability = 79
    4.1 Separable Polynomials = 79
    4.2 Separable Degree = 81
    4.3 The Simple Case = 82
    4.4 The Finite Case = 84
    4.5 The Algebraic Case = 87
    4.6 Pure Inseparability = 88
    4.7 Separable and Purely Insparable Closures = 91
    4.8 Perfect Fields = 94
Part 2 Galois Theory = 99
  Chapter 5 Galois Theory Ⅰ = 101
    5.1 Galois Connections = 101
    5.2 The Galois Correspondence = 104
    5.3 Who's Closed? = 109
    5.4 Normal Subgroups and Normal Extensions = 112
    5.5 More on Galois Groups = 113
    5.6 Linear Disjointness = 117
    5.7 The Krull Topology = 120
  Chapter 6 Galois Theory Ⅱ = 127
    6.1 The Galois Group of a Polynomial = 127
    6.2 Symmetric Polynomials = 128
    6.3 The Discriminant of a Polynomial = 132
    6.4 The Galois Groups of Some Small Degree Polynomials = 134
  Chapter 7 A Field Extension as a Vector Space = 147
    7.1 The Norm and the Trace = 147
    7.2 The Discriminant of Field Elements = 151
    7.3 Algebraic Independence of Embeddings = 155
    7.4 The Normal Basis Theorem = 156
  Chapter 8 Finite Fields Ⅰ : Basic Properties = 161
    8.1 Finite Fields = 161
    8.2 Finite Fields as Splitting Fields = 162
    8.3 The Subfields of a Finite Field = 163
    8.4 The Multiplicative Structure of a Finite Field = 163
    8.5 The Galois Group of a Finite Field = 165
    8.6 Irreducible Polynomials over Finite Fields = 165
    8.7 Normal Bases = 169
    8.8 The Algebraci Closure of a Finite Field = 170
  Chapter 9 Finite Fields Ⅱ : Additonal Properties = 175
    9.1 Finte Field Arithmetic = 175
    9.2 The Number of Irreducible Polynomials = 178
    9.3 Polynomial Functions = 180
    9.4 Linearized Polynomials = 182
Part 3 The Theory of Binomials = 187
  Chapter 10 The Roots of Unity = 189
    10.1 Roots of Unity = 189
    10.2 Cyclotomic Extensions = 191
    10.3 Normal Bases and Roots of Unity = 198
    10.4 Wedderburn's Theorem = 200
    10.5 Realizing Groups as Galois Groups = 201
  Chapter 11 Cyclic Extensions = 209
    11.1 Cyclic Extensions = 210
    11.2 Extensions fo Degree Char(F) = 212
  Chapter 12 Solvable Extensions = 215
    12.1 Solvable Groups = 215
    12.2 Solvable Extensions = 216
    12.3 Solvability by Radicals = 219
    12.4 Polynomial Equations = 222
  Chapter 13 Binomials = 227
    13.1 Irreducibility = 228
    13.2 The Galois Group of a Binomial = 232
    13.3 The Independence of Irrational Numbers = 241
  Chapter 14 Families of Binomials = 247
    14.1 The Splitting Field = 247
    14.2 Kummer Theory = 249
Appendix M o ·· bius Inversion = 257
References = 265
Index of Symbols = 267
Index = 269

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