环和模的范畴 第2版（影印版）

　　This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the familiarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules.
　　

preface
o. preliminaries
chapter 1: rinos, modules and homomorphisms
1. review of rings and their homomorphisms
2. modules and submodules
3. homomorphisms of modules
4. categories of modules; endomorphism rings
chapter 2: direct sums and products
5. direct summands
6. direct sums and products of modules
7. decomposition of rings
8. generating and cogenerating
chapter 3: finiteness conditions for modules
9. semisimple modules--the socle and the radical
10. finitely generated and finitely cogenerated modules-chain conditions
11. modules with composition series
12. indecomposable decompositions of modules
chapter 4: classical ring-structure theorems
13. semisimple rings
14. the density theorem

　　This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the familiarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules.
　　 Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the horn and tensor functions, Morita equivalence and duality, decomposition theory of injective and projective modules, and semiperfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have helped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course, many important areas of ring and module theory that the text does not touch upon. For example, we have. made no attempt to cover such subjects as homology, rings of quotients, or commutative ring theory.
　　 This book has evolved from our lectures and research over the past several years. We are deeply indebted to many of our students and colleagues for their ideas and encouragement during its preparation. We extend our sincere thanks to them and to the several people who have helped with the preparation of the manuscripts for the first two editions, and/or pointed out errors in the first.
　　 Finally, we apologize to the many authors whose works we have used but not specifically cited. Virtually all of the results in this book have appeared in some form elsewhere in the literature, and they can be found either in the books and articles that are listed in our bibliography, or in those listed in the collective bibliographies of our citations.
　　Eugene, OR
　　Frank W. Anderson
　　Iowa City, IA
　　Kent R. Fuller
　　January 1992