Lifting Modules

Supplements and Projectivity in Module Theory

  • John Clark
  • Christian Lomp
  • Narayanaswami Vanaja
  • Robert Wisbauer

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pages 1-53
  3. Pages 207-264
  4. Back Matter
    Pages 359-394

About this book

Introduction

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules.

The text begins with an introduction to small submodules, the radical, variations on projectivity, and hollow dimension. The subsequent chapters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange property and local semi-T-nilpotency), supplements in modules (with specific emphasis on semilocal endomorphism rings), finishing with a long chapter on lifting modules, leading up their use in the theory of perfect rings, Harada rings, and
quasi-Frobenius rings.

Most of the material in the monograph appears in book form for the first time. The main text is augmented by a plentiful supply of exercises together with comments on further related material and on how the theory has evolved.

Keywords

Morphism algebra lifting module module theory torsion

Authors and affiliations

  • John Clark
    • 1
  • Christian Lomp
    • 2
  • Narayanaswami Vanaja
    • 3
  • Robert Wisbauer
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  2. 2.Departamento de Matemática Pura, Faculdade de CiênciasUniversidade do PortoPortoPortugal
  3. 3.Department of MathematicsUniversity of MumbaiMumbayIndia
  4. 4.Institute of MathematicsHeinrich Heine University DüsseldorfDüsseldorfGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-7643-7573-6
  • Copyright Information Birkhäuser Verlag 2006
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7572-0
  • Online ISBN 978-3-7643-7573-7
  • Series Print ISSN 1660-8046
  • About this book