Preface 1.What is Algebra? 2.Fields 3.Commutative Rings 4.Homomorphisms and Ideals 5.Modules 6.Algebraic Aspects of Dimension 7.The Algebraic View of Infinitesimal Notions 8.Noncommutative Rings 9.Modules over Noncommutative Rings 10.Semisimple Modules and Rings 11.Division Algebras of Finite Rank 12.The Notion of a Group 13.Examples of Groups: Finite Groups 14.Examples of Groups: Infinite Discrete Groups 15.Examples of Groups: Lie Groups and Algebraic Groups 16.General Results of Group Theory 17.Group Representations A.Representations of Finite Groups B.Representations of Compact Lie Groups 18.Some Applications of Groups A.Galois Theory B.The Galois Theory of Linear Differential Equations (Picard Vessiot Theory) C.Classification of Unramified Covers D.Invariant Theory E.Group Representations and the Classification of Elementary Particles 19.Lie Algebras and Nonassociative Algebra A.Lie Algebras B.Lie Theory C.Applications of Lie Algebras D.Other Nonassociative Algebras 20.Categories 21.Homological Algebra A.Topological Origins of the Notions of Homological Algebra B.Cohomology of Modules and Groups C.Sheaf Cohomology 22.K—theory A.Topological K—theory B.Algebraic K—theory Comments on the Literature References Index of Names Subject Index
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