Lifting Modules Supplements and Projectivity in Module Theory /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Clark, John (Autor), Lomp, Christian (Autor), Vanaja, N. (Autor), Wisbauer, Robert (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2006.
Edición:1st ed. 2006.
Colección:Frontiers in Mathematics,
Temas:
Algebra.
Acceso en línea:Texto Completo

MARC

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100 1 |a Clark, John.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Lifting Modules  |h [electronic resource] :  |b Supplements and Projectivity in Module Theory /  |c by John Clark, Christian Lomp, N. Vanaja, Robert Wisbauer. 
250 |a 1st ed. 2006. 
264 1 |a Basel :  |b Birkhäuser Basel :  |b Imprint: Birkhäuser,  |c 2006. 
300 |a XIII, 394 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 1 |a Frontiers in Mathematics,  |x 1660-8054 
505 0 |a Basic notions -- Preradicals and torsion theories -- Decompositions of modules -- Supplements in modules -- From lifting to perfect modules. 
520 |a 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. 
650 0 |a Algebra. 
650 1 4 |a Algebra. 
700 1 |a Lomp, Christian.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Vanaja, N.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Wisbauer, Robert.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783764391249 
776 0 8 |i Printed edition:  |z 9783764375720 
830 0 |a Frontiers in Mathematics,  |x 1660-8054 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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