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Lifting Modules : Supplements and Projectivity in Module Theory /

By: Clark, John [author.].
Contributor(s): Lomp, Christian [author.1] | Vanaja, Narayanaswami [author.1] | Wisbauer, Robert [author.2] | SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Frontiers in Mathematics.Publisher: Basel : Birkh�user Basel, 2006. Description: XIII, 394 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764375737.Subject(s): Mathematics | Algebra.1 | Mathematics.2 | Algebra.1DDC classification: 512 Online resources: Click here to access online
Contents:
Basic notions -- Preradicals and torsion theories -- Decompositions of modules -- Supplements in modules -- From lifting to perfect modules.
In: Springer eBooks0Summary: 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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PK Kelkar Library, IIT Kanpur
Available EBK7969
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Basic notions -- Preradicals and torsion theories -- Decompositions of modules -- Supplements in modules -- From lifting to perfect modules.

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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