Lifting Modules

John Clark

ISBN 10: 3764375728 / ISBN 13: 9783764375720

Verlag: Springer, Basel, Birkhäuser Basel, Birkhäuser Jul 2006, 2006

Beschreibung

This item is printed on demand - it takes 3-4 days longer - Neuware -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, andquasi-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. 394 pp. Englisch.

Bestandsnummer des Verkäufers 9783764375720

Bibliografische Details

• Titel: Lifting Modules
• Verlag: Springer, Basel, Birkhäuser Basel, Birkhäuser Jul 2006
• Erscheinungsjahr: 2006
• Sprache: Englisch
• ISBN-10: 3764375728
• ISBN-13: 9783764375720
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 240B x 192 H x 36 T Millimeter Breite: 240 mm, Höhe: 192 mm, Tiefe: 36 mm
• Gewicht: 790 Gramm

Über diesen Titel

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.

Von der hinteren Coverseite

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.