【图书简介】
本书论述代数学及其在现代数学和科学中的地位，高度原创且内容充实。作者通过讨论大学代数课程，如李群、上同调、范畴论等，阐述每个代数概念的起源与物理现象及其他数学分支之间的联系。本书为数学家必读，无论他是初学代数学还是代数学专家。
目录
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.
18. Some Applications of Groups.
19. Lie Algebras and Nonassociative Algebra.
20. Categories.
21. Homological Algebra
22. K-theory
Comments on the Literature.
References.
Index of Names
Subject Index
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