模与环讲义 英文影印版
作者：（美）拉姆 著
出版时间：2012年版
内容简介
拉姆编著的《模与环讲义》是一部完全独立与作者早期有关的研究生教材，另外一本讲述模和环理论的入门书籍，是以作者近些年在berkeley大学的讲义为蓝本发展而来。这本书既适用于研究生教材和更高层次的科研人员，也可用作的自学材料或者一般参考资料。书的侧重点强调模和环的几个重要方面，运用有效的方法将读者直接引入书的基本核心和有用观点。内容包括自由模、射影模、单射模和平坦模、有限条件ore局部化、非奇异环和goldie定理、商环鞅和最大化、frobenius和伪-frobenius环和模范畴等价性和对偶性的经典morito理论。读者对象：数学专业的本科生、研究生、自学人员和相关科研人士。
目录
Preface
Notes to the Reader
Partial List of Notations
Partial List of Abbreviations
1 Free Modules， Projective， and Injective Modules
1. Free Modules
1A. Invariant Basis Number （IBN）
1B. Stable Finiteness
1C. The Rank Condition
1D. The Strong Rank Condition
1E. Synopsis
Exercises for 1
2. Projective Modules
2A. Basic Definitions and Examples
2B. Dual Basis Lemma and Inveriible Modules
2C. Invertible Fraaional Ideals
2D. The Picard Group of a Commutative Ring
2E. Hereditary and Semihereditary Rings
2F. Chase Small Examples
2G. Hereditary Artinian Rings
2H. Trace Ideals
Exercises for 2
3. Injective Modules
3A. Baer's Test for Injectivitv
3B. Self-Iniective Rings
3C. Injectivity versus Divisibility
3D. Essential Extensions and Injective Hulls
3E. Injectives over Right Noetherian Rings
3F. Indecomposable Injectives and Uniform Modules
3G. Injectives over Some Artinian Rings
3H. Simple Injcctives
3I. Matlis' Theory
3J. Some Computations oflnjective Hulls
3K. Applications to Chain Conditions
Exercises for 3
2 Flat Modules and Homological Dimensions
4. Flat and Faithfully Flat Modules
4A. Basic Properties and Flatness Tests
4B. Flatness， Torsion-Freeness， and von Neumann Regularity
4C. More Flatness Tests
4D. Finitely Presented （f.p.） Modules
4E. Finitely Generated Flat Modules
4F. Direct Products of Flat Modules
4G. Coherent Modules and Coherent Rings
4H. Semihereditary Rings Revisited
4I. Faithfully Flat Modules
4J. Pure Exact Sequences
Exercises for 4
5. Homological Dimensions
5A. Schanuel's Lemma and Projective Dimensions
5B. Change of Rings
5C. Injectivc Dimensions
5D. Weak Dimensions of Rings
5E. Global Dimensions of Semiprimary Rings
5F. Global Dimensions of Local Rings
5G. Global Dimensions ofCommutative Noetherian Rings
Exercises for 5
3 More Theory of Modules
4 Rings of Quotients
5 More Rings of Quotients
6 Frobenius and Quasi-Frobenius Rings
7 Matrix Rings， Categories of Modules， and Morita Theory
References
Name Index
Subject Index
