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Lifting Modules: Supplements and Projectivity in Module Theory
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Lifting Modules: Supplements and Projectivity in Module Theory Paperback - 2006

by John Clark; Christian Lomp; N. Vanaja

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From the publisher

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.

First line

For basic definitions, theorems and notation, we refer the reader to texts in Module Theory, mainly to [363] and [85] and occasionally to [13], [100], and [189].

From the rear cover

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.

Details

  • Title Lifting Modules: Supplements and Projectivity in Module Theory
  • Author John Clark; Christian Lomp; N. Vanaja
  • Binding Paperback
  • Edition N/A
  • Pages 394
  • Volumes 1
  • Language ENG
  • Publisher Birkhauser, Basel
  • Publication date 2006-07-18
  • Illustrated Yes
  • Features Bibliography, Illustrated, Index, Table of Contents
  • ISBN 9783764375720 / 3764375728
  • Weight 1.75 lbs (0.79 kg)
  • Dimensions 9.4 x 6.6 x 0.8 in (23.88 x 16.76 x 2.03 cm)
  • Category Mathematics
  • Library of Congress Catalogue Number 2006047645
  • Dewey Decimal Code 510
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