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Flat Covers of Modules

  • Book
  • © 1996

Overview

Authors:
  1. Jinzhong Xu
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1634)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Jinzhong Xu
    Pages 1-3

  3. Envelopes and covers

    • Jinzhong Xu
    Pages 5-25

  4. Fundamental theorems

    • Jinzhong Xu
    Pages 27-50

  5. Flat covers and cotorsion envelopes

    • Jinzhong Xu
    Pages 51-79

  6. Flat covers over commutative rings

    • Jinzhong Xu
    Pages 81-106

  7. Applications in commutative rings

    • Jinzhong Xu
    Pages 107-151

  8. Back Matter

    Pages 153-162
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Flat Covers of Modules

  • Authors: Jinzhong Xu

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094173

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1996

  • Softcover ISBN: 978-3-540-61640-5Published: 02 October 1996

  • eBook ISBN: 978-3-540-69992-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 162

  • Topics: K-Theory

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