代數(shù)學(xué)基礎(chǔ)

內(nèi)容概要

本書論述代數(shù)學(xué)及其在現(xiàn)代數(shù)學(xué)和科學(xué)中的地位，高度原創(chuàng)且內(nèi)容充實。作者通過討論大學(xué)代數(shù)課程，如李群、上同調(diào)、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(xué)分支之間的聯(lián)系。本書為數(shù)學(xué)家必讀，無論他是初學(xué)代數(shù)學(xué)還是代數(shù)學(xué)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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