John Clark

(Author)

Lifting Modules: Supplements and Projectivity in Module Theory (2006)Paperback - 2006, 18 July 2006

Lifting Modules: Supplements and Projectivity in Module Theory (2006)
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Part of Series
Frontiers in Mathematics
Print Length
394 pages
Language
English
Publisher
Birkhauser
Date Published
18 Jul 2006
ISBN-10
3764375728
ISBN-13
9783764375720

Description

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.

Product Details

Authors:
John ClarkChristian LompN VanajaRobert Wisbauer
Book Edition:
2006
Book Format:
Paperback
Country of Origin:
DE
Date Published:
18 July 2006
Dimensions:
23.88 x 16.76 x 2.03 cm
ISBN-10:
3764375728
ISBN-13:
9783764375720
Language:
English
Location:
Basel
Pages:
394
Publisher:
Weight:
793.79 gm

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