Flat Covers of Modules
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 conj
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1634
Springer
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Jinzhong Xu
Flat Covers of Modules
Springer
Author Jinzhong Xu University of Kentucky Department of Mathematics Lexington, Kentucky, 40506-0027 USA
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Xu, Jinzhong: Flat covers or modules I Jinzhong Xu. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1996 (Lecture notes in mathematics; 1634) ISBN 3-540-61640-3
NE:GT
Mathematics Subject Classification (1991): l3CII, 13C15, 13E05, 13D05, 13HI0, l6A50, 16A52, 16A62, 18A30, 18G05, 18G15, 18G25, ISSN 0075-8434 ISBN 3-540-61640-3 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer- Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1996 Printed in Germany
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10479845 46/3142-543210 - Printed on acid-free paper
Dedicated to
Professor Edgar E. Enochs My Mother Guizhen Zhu and
My Father Youcheng Xu
Acknowledgement Professor Enochs introduced me to the subject of flat covers five years ago. He also encouraged me to write this monograph two years ago when we made substantial progress in the theory of flat covers. I sincerely thank him for his constant encouragement and adivce. In fact, I have just reorganized and rewritten some of his work in many parts of this monograph. I am grateful to the referees for their careful reading and useful suggestions. Using their reports and advice, I have been able to improve the original draft and remove some flaws. Now it is the time for me to thank all the people who helped me both academically and nonacademically for so many years. In particular, I would like to thank Mrs. Louise Enochs for her kind care and help. Each time she invited me and other students to have dinner with their family, we just felt like family members. I especially did. I thank Professor Foxby who gave me his encouragement when I asked him questions about Gorenstein modules and Gorenstein rings. I would also like to thank Professor Vasconcelos who has encouraged so many young people like me. I a
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