Flat Covers of Modules

Jinzhong Xu (auth.)9783540616405, 3-540-61640-3

Since the injective envelope and projective cover were defined by Eckmann and Bas in the 1960s, they have had great influence on the development of homological algebra, ring theory and module theory. In the 1980s, Enochs introduced the flat cover and conjectured that every module has such a cover over any ring. This book provides the uniform methods and systematic treatment to study general envelopes and covers with the emphasis on the existence of flat cover. It shows that Enochs’ conjecture is true for a large variety of interesting rings, and then presents the applications of the results. Readers with reasonable knowledge in rings and modules will not have difficulty in reading this book. It is suitable as a reference book and textbook for researchers and graduate students who have an interest in this field.

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Table of contents :
Introduction….Pages 1-3
Envelopes and covers….Pages 5-25
Fundamental theorems….Pages 27-50
Flat covers and cotorsion envelopes….Pages 51-79
Flat covers over commutative rings….Pages 81-106
Applications in commutative rings….Pages 107-151