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  代数学（英文版）
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• Contents
  Preface
  Chapter 1 Groups 1
  1.1 Semigroups, monoids and groups 1
  1.2 Subgroups 6
  1.3 Theactionofagrouponaset 11
  1.4 The Sylow theorem 18
  1.5 Homomorphisms and normal subgroups 20
  1.6 Direct products and direct sums 29
  1.7 Simple groups 36
  1.8 Nilpotent groups and solvable groups 39
  Chapter 2 Modules 44
  2.1 Rings and ring homomorphisms 44
  2.2 Modules and free modules 55
  2.3 Projectivemodulesandinjectivemodules 67
  2.4 Homologicaldimensionsandsemisimplerings 75
  2.5 Tensor product and weak dimension 83
  2.6 Localization 95
  2.7 Noetherian modules and UFD 104
  2.8 Finitely generated modules over a PID 115
  Chapter 3 Fields and Galois Theory of Equations 129
  3.1 Extensionsof elds 129
  3.2 Splitting elds, and normality 137
  3.3 ThemaintheoremofGaloistheory 147
  3.4 Modules and free modules 55
  3.5 Constructionwithstraight-edgeandcompass 157
  3.6 The Hilbert Nullstellensatz 160
  Chapter 4 Introduction of Various Algebras 167
  4.1 Associativealgebras 167
  4.2 CoassociativecoalgebrasandHopfalgebras 178
  4.3 Nonassociative algebras 182
  Chapter 5 Category 193
  5.1 Category: Direct limits and colimits 193
  5.2 Functors and natural transformations 198
  5.3 Abelian categories and homological groups 207
  Bibliography 217
  Index 219