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Lifting Modules

Supplements and Projectivity in Module Theory
Buch | Softcover
XIII, 394 Seiten
2006 | 2006
Springer Basel (Verlag)
978-3-7643-7572-0 (ISBN)

Lese- und Medienproben

Lifting Modules - John Clark, Christian Lomp, N. Vanaja, Robert Wisbauer
CHF 82,35 inkl. MwSt

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.

Basic notions.- Preradicals and torsion theories.- Decompositions of modules.- Supplements in modules.- From lifting to perfect modules.

Erscheint lt. Verlag 18.7.2006
Reihe/Serie Frontiers in Mathematics
Zusatzinfo XIII, 394 p.
Verlagsort Basel
Sprache englisch
Maße 168 x 240 mm
Gewicht 785 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte Algebra • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • lifting module • module theory • Modul (math.) • Morphism • Torsion
ISBN-10 3-7643-7572-8 / 3764375728
ISBN-13 978-3-7643-7572-0 / 9783764375720
Zustand Neuware
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