Authors:
- First comprehensive monograph devoted to results around lifting modules
- Basic notions and techniques from module theory are reviewed, in particular various observations around (weakly) supplemented and semilocal modules and projectivity conditions; these are applied to investigate decomposition features of lifting modules, discrete and quasi-discrete modules, and semiperfect modules
- Includes supplementary material: sn.pub/extras
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand
John Clark
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Departamento de Matemática Pura, Faculdade de Ciências, Universidade do Porto, Porto, Portugal
Christian Lomp
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Department of Mathematics, University of Mumbai, Mumbay, India
Narayanaswami Vanaja
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Institute of Mathematics, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
Robert Wisbauer
Bibliographic Information
Book Title: Lifting Modules
Book Subtitle: Supplements and Projectivity in Module Theory
Authors: John Clark, Christian Lomp, Narayanaswami Vanaja, Robert Wisbauer
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/3-7643-7573-6
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2006
Softcover ISBN: 978-3-7643-7572-0Published: 18 July 2006
eBook ISBN: 978-3-7643-7573-7Published: 17 August 2008
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XIII, 394
Topics: Algebra