Lifting Modules : Supplements and Projectivity in Module Theory
- Author
- John Clark, Christian Lomp, Narayanaswami Vanaja, …
- Publication Year
- 2006
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
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.
Keywords: Mathematics and Statistics / Morphism / Algebra / Lifting module / Module theory / Torsion
