Item description for Lifting Modules: Supplements and Projectivity in Module Theory (Frontiers in Mathematics) by John Clark...
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.
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Est. Packaging Dimensions: Length: 9.37" Width: 6.69" Height: 0.87" Weight: 1.85 lbs.
Release Date Aug 29, 2006
Publisher Birkhäuser Basel
ISBN 3764375728 ISBN13 9783764375720
Availability 129 units. Availability accurate as of Mar 27, 2017 12:45.
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More About John Clark
John Clark is Chief Executive Officer of the University of Western Sydney, Hawskbury. He was previously Director of the Speech, Hearing and Language Centre at Macquarie University, Sydney.
Colin Yallop is Associate Professor in Linguistics at Macquarie and is Director of the University's Dictionary Research Centre.