Lifting Modules [electronic resource] :Supplements and Projectivity in Module Theory / by John Clark, Christian Lomp, Narayanaswami Vanaja, Robert Wisbauer.
by Clark, John [author.]; Lomp, Christian [author.]; Vanaja, Narayanaswami [author.]; Wisbauer, Robert [author.]; SpringerLink (Online service).
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BookSeries: Frontiers in Mathematics: Publisher: Basel : Birkhäuser Basel, 2006.Description: XIII, 394 p. online resource.ISBN: 9783764375737.Subject(s): Mathematics | Algebra | Mathematics | AlgebraDDC classification: 512 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA150-272 (Browse shelf) | Available |
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| QA1-939 Symmetry | QA370-380 Variational Problems in Materials Science | QA241-247.5 Value Distribution Theory Related to Number Theory | QA150-272 Lifting Modules | QA319-329.9 Theory of Function Spaces III | RM1-950 Clinical Trial Registries | QA329-329.9 Wavelets, Multiscale Systems and Hypercomplex Analysis |
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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