Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.

Injective modules (Algebra) --- Projective modules (Algebra) --- Representations of rings (Algebra) --- Decomposition (Mathematics) --- Mathematics --- Probabilities --- Rings (Algebra) --- Modules (Algebra)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Modules (Algebra) --- Moduli theory. --- Projective modules (Algebra) --- Ideals (Algebra) --- Modules (Algèbre) --- Variétés topologiques à 4 dimensions --- Idéaux (Algèbre) --- Ideals (Algebra). --- Modules (Algebra). --- Projective modules (Algebra). --- Moduli theory --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Algebraic ideals --- Theory of moduli --- Finite number systems --- Modular systems (Algebra) --- Mathematics. --- Algebra. --- Mathematical analysis --- Math --- Science --- Algebraic fields --- Rings (Algebra) --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Finite groups