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Lifting modules - Supplements and Projectivity in Module Theory

Title
Lifting modules - Supplements and Projectivity in Module Theory
Type
Book
Year
2006
Authors
Christian Lomp
(Author)
FCUP
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John Clark
(Author)
Other
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N. Vanaja
(Author)
Other
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Robert Wisbauer
(Author)
Other
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Indexing
Publicação em Scopus Scopus
Scientific classification
FOS: Natural sciences > Mathematics
CORDIS: Physical sciences > Mathematics > Algebra
Other information
Resumo (PT): 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.
Abstract (EN): 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.
Language: English
Type (Professor's evaluation): Scientific
Contact: http://www.springer.com/birkhauser/mathematics/book/978-3-7643-7572-0
No. of pages: 394
ISBN: 978-3-7643-7572-0
Collection: Frontiers in Mathematics
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Publications included
Chapter or Part of a Book
clark, john (Author) (Other); lomp, christian (Author) (FCUP); vanaja, narayanaswami (Author) (Other); wisbauer, robert (Author) (Other)
Chapter or Part of a Book
Clark, John (Author) (Other); Lomp, Christian (Author) (Other); Vanaja, Narayanaswami (Author) (Other); Wisbauer, Robert (Author) (Other)
Chapter or Part of a Book
Clark, John (Author) (Other); Lomp, Christian (Author) (Other); Vanaja, Narayanaswami (Author) (Other); Wisbauer, Robert (Author) (Other)
Chapter or Part of a Book
Clark, John (Author) (Other); Lomp, Christian (Author) (Other); Vanaja, Narayanaswami (Author) (Other); Wisbauer, Robert (Author) (Other)
Chapter or Part of a Book
Clark, John (Author) (Other); Lomp, Christian (Author) (Other); Vanaja, Narayanaswami (Author) (Other); Wisbauer, Robert (Author) (Other)
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