000 02227nam a22002177a 4500
003 OSt
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008 190424b ||||| |||| 00| 0 eng d
020 _a9783662387535
040 _cTata Book House
_aICTS-TIFR
050 _aQA154.2
100 _aShafarevich I. R.
245 _aAlgebra I
_b : basic notions of algebra
260 _aNew York:
_bSpringer Verlag,
_c[c1990]
300 _a258 p
490 _aEncyclopedia of Mathematical Sciences
_vVol. 11
505 _a1. 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
520 _aThis 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
856 _uhttps://doi.org/10.1007/978-3-662-39643-8
942 _2lcc
_cBK
999 _c2643
_d2643