TY  - BOOK
AU  - Shafarevich I. R. 
TI  - Algebra I:  : basic notions of algebra
T2  - Encyclopedia of Mathematical Sciences
SN  - 9783662387535
AV  - QA154.2 
PY  - 1990///]
CY  - New York
PB  - Springer Verlag
N1  - 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
N2  - This book aims to present a general survey of algebra, of its basic notions and main branches. Now what language should we choose for this? In reply to the question ‘What does mathematics study?’, it is hardly acceptable to answer ‘structures’ or ‘sets with specified relations’; for among the myriad conceivable structures or sets with specified relations, only a very small discrete subset is of real interest to mathematicians, and the whole point of the question is to understand the special value of this infinitesimal fraction dotted among the amorphous masses. In the same way, the meaning of a mathematical notion is by no means confined to its formal definition; in fact, it may be rather better expressed by a (generally fairly small) sample of the basic examples, which serve the mathematician as the motivation and the substantive definition, and at the same time as the real meaning of the notion.---summary provided by publisher
UR  - https://doi.org/10.1007/978-3-662-39643-8
ER  -