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Basic Notions of Algebra
von: Igor R. Shafarevich, Aleksej I. Kostrikin, Igor R. Shafarevich
Springer-Verlag, 2005
ISBN: 9783540264743 , 260 Seiten
Format: PDF, OL
Kopierschutz: DRM
Preis: 171,19 EUR
Contents
5
Preface
8
§ 1. What is Algebra?
10
§ 2. Fields
15
§ 3. Commutative Rings
21
§ 4. Homomorphisms and Ideals
28
§ 5. Modules
37
§ 6. Algebraic Aspects of Dimension
45
§ 7. The Algebraic View of Infinitesimal Notions
54
§ 8. Noncommutative Rings
65
§ 9. Modules over Noncommutative Rings
78
§ 10. Semisimple Modules and Rings
83
§ 11. Division Algebras of Finite Rank
94
§ 12. The Notion of a Group
100
§ 13. Examples of Groups: Finite Groups
112
§ 14. Examples of Groups: Infinite Discrete Groups
128
§ 15. Examples of Groups: Lie Groups and Algebraic Groups
144
§ 16. General Results of Group Theory
155
§ 17. Group Representations
164
§ 18. Some Applications of Groups
181
§ 19. Lie Algebras and Nonassociative Algebra
192
§ 20. Categories
206
§ 21. Homological Algebra
217
§ 22. X-theory
234
Comments on the Literature
243
References
248
Index of Names
253
Subject Index
255
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