Lifting Modules: Supplements and Projectivity in Module Theory (Frontiers in Mathematics) - Softcover

Buch 10 von 48: Frontiers in Mathematics

Clark, John

 
9783764375720: Lifting Modules: Supplements and Projectivity in Module Theory (Frontiers in Mathematics)
Softcover
ISBN 10: 3764375728 ISBN 13: 9783764375720
Verlag: Birkhäuser Basel, 2006

Inhaltsangabe

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

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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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Verlag
Birkhäuser Basel
Erscheinungsdatum
2006
Sprache
Englisch
ISBN 10 
3764375728
ISBN 13 
9783764375720
Einband
Taschenbuch
Anzahl der Seiten
412
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