代數(shù)學基礎

內容概要

本書論述代數(shù)學及其在現(xiàn)代數(shù)學和科學中的地位，高度原創(chuàng)且內容充實。作者通過討論大學代數(shù)課程，如李群、上同調、范疇論等，闡述每個代數(shù)概念的起源與物理現(xiàn)象及其他數(shù)學分支之間的聯(lián)系。本書為數(shù)學家必讀，無論他是初學代數(shù)學還是代數(shù)學專家。

書籍目錄

Preface1. What is Algebra?2. Fields3. Commutative Rings4. Homomorphisms and Ideals5. Modules6. Algebraic Aspects of Dimension7. The Algebraic View of Infinitesimal Notions8. Noncommutative Rings9. Modules over Noncommutative Rings10. Semisimple Modules and Rings11. Division Algebras of Finite Rank12. The Notion of a Group13. Examples of Groups: Finite Groups14. Examples of Groups: Infinite Discrete Groups15. Examples of Groups: Lie Groups and Algebraic Groups16. General Results of Group Theory17. Group Representations18. Some Applications of Groups19. Lie Algebras and Nonassociative Algebra20. Categories21. Homological Algebra22. K-theoryComments on the LiteratureReferencesIndex of NamesSubject Index

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