基本同调代数

《基本同调代数》是2003年6月1日由世界图书出版公司出版的书籍。本书用英文介绍了基本同调代数的概念、作用、定理、运算方法、适用范围等内容。

• 中文名 基本同调代数
• 别名 basic homological algebra
• 出版社 世界图书出版公司
• 出版时间 2003年6月1日
• 装帧 平装

内容简介

　　《基本周调代数(英文版)》内容简介:Fiveyearsago,Itaughtaone-quartercourseinhomologicalalgebra.Idiscoveredthattherewasnobook来自whichwasreallysuitableasatextforsuchashortcourse,soIdecidedtowriteone.ThepointwastocoverbothExtandTotearly,andstillhaveenoughmaterialforalargercourse(onesemesterortwoquarter抗愿s)goingoffinanyofseveralpossibledirections.Thisbookis'alsointendedtobereadableenoughforindependentstudy. {zzjj}

目录

　　360百科Preface

　　1 Categories

　　2 Modules

　请境代始谓蒸明　2.1 Generalities

　　2.2 Tensor Products

　　2.3 Exactness of Functors

　　2.4 Projectives, Injectives, and Flats

　　3 Ext and Tor

　　3.1 Complex岁织es and Projective Resol消utions

　　3.2 Long 星太Exact Sequences

　　3.3 Flat Resolutions and Injective Resolutions

　　3.4 Consequences

　　4 Dimension Theory

　　4.1 Dimension Shifting

　　使欢足妒无制4.2 When Flats are Projective

　　4.3 Dimension Zero

　　4.4 An Example

　　5 Change of Rings

　　5.1 C冲客尔久罗omputational Considerations

　　5.2 Matrix Ri积模杆ngs

　　5.3 Poly造其资思nomials

　　5.4 Qu货燃保夜端刑端几若明otients and Localization

　　6 Derived Functors

　　6.1 Additive Functors

　　6.2 图身使结钟活土凯西Derived Functors

　　6.3 Long Exact Sequences小--Ⅰ. Existence

　　6.4 Long Exact Sequences--Ⅱ. Naturality

　　6.5 Long Exact Sequences--阳皮县Ⅲ. Weirdness

　　6.6 Universality of Ext

　　7 Abstract Homological Algebra

　　7.1 Living Without Elements

　　7.2 Additive Categories

　　7.3 Kernels and Cokernels

　　7.4 Cheating with Projectives

　　7.5 (Interlude) Arrow Categ小叫马千操走副几非ories

　　7.6 H强omology in Abelia钟是结南饭季革考织n Categories

　　7.7 Long Exact'Sequences

　　7.8 An Alternative fo春践r Unbalanced Categories

　　8 Colimits and Tor

　　8.1 Limits and Colimits

　　8.2 Adjoint Functors

　　8.3 Directed Colimits and Tor

　　8.4 Lazard's Theorem

　　8.5 Weak Dimension Revisited

　　9 毛析Odds and Ends

　　9.1 Injective Envelopes

　　9.2 UniVersal Coefficients

　　9.3 The Kiinneth Theorems

　　9.4 Do Connecting Homomorphisms Commute?

　　9.5 The Ext Product

　　9.6 The 3acobson Radical, Nakayama's Lemma, and Quasilocal Rings

　　9.7 Local Rings and Localization Revisited (Expository)

　　A GCDs, LCMs, PIDs, and UFDs

　　B The Ring of Entire Functions

　　C The Mitchell-Freyd Theorem and Cheating in Abelian Cat egories

　　D Noether Correspondences in Abelian Categories

　　Solution Outlines

　　References

　　Symbol Index

　　Index

丛书信息

　　Graduate Texts 严底投诗任收有础in Mathematics (共158册), 这套丛书还有 《加性数论》,《复变导论》,《概率论(第1卷)》,《偏微分方程.第2版》,《黎曼曲面》 等。