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 ...
This presentation covers known and new results on extending modules and related notions. An extending module is a module for which every submodule is essential in a direct summand. Semisimple modules, uniform modules and injective modules are examples of extending modules.
In the preface of this book, the authors express the view that 'a good working knowledge of injective modules is a sound investment for module theorists'. The existing literature on the subject has tended to deal with the applications of injective modules to ring theory. The aim of this tract is to demonstrate some of the applications of injective ...
This book examines a topic from the theory of residues and duality. For broad classes of local algebras $f:R\rightarrow S$ and an $R$-module $M$ of zero dimensional support, Huang provides various canonical constructions of an $S$-module of zero dimensional support. Canonical isomorphisms between the various approaches are given using the residue ...
These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely ...
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