This volume provides a comprehensive introduction to module theory and the related part of
ring theory, including original results as well as the most recent work. It is a useful and …

Continuous and discrete modules are, essentially, generalizations of infective and projective
modules respectively. Continuous modules provide an appropriate setting for decomposition …

Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

Page 1 PURE AND APPLIED MATHEMATICS A Series of Monographs and Textbooks LINEAR
ALGEBRA OVER COMMUTATIVE RINGS Bernard R. McDonald Page 2 Linear Algebra Over …

This survey covers material in Referativnyi Zhurnal Matematika and is a continuation of AV
Mikhalev's survey in Algebra. Topology. Geometry, Vol. 12 (Itogi Nauki i Tekhniki (1974)) …

A ring A is an exchange ring if the following two equivalent conditions hold:(1) for any
element a∈ A, there exists an idempotent e∈ aA with 1− e∈(1− a) A;(2) for any element a∈ …

Matrix methods of elementary linear algebra are extended to general direct-sum
decompositions of modules. These methods are then shown to yield simple proofs of some …

An independence structure on indecomposable modules Page 1 An independence structure
on indecomposable modules Istwin Beck*) Introduction A module A is called an Le-module …

Publisher Summary This chapter discusses the modules, along with the exchange property
and exchange rings. All rings are assumed to be associative and unital. If A is a ring, then J …

A module M is said to complement direct summands if every direct summand of M has the
exchange property with respect to completely indecomposable modules, or in other words if …