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 …

A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

This expository monograph was written for three reasons. Firstly, we wanted to present the
solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we …

An associative ring R with identity is semiperfect if and only if every element of R is a sum of
a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring …

Bass [1] proved that if R is a left perfect ring, then R contains no infinite sets of orthogonal
idempotents and every nonzero left R-module has a maximal submodule, and asked if this …

A separative ring is one whose finitely generated projective modules satisfy the property A⊕
A⋟ A⊕ B⋟ B⊕ B⇒ A⋟ B. This condition is shown to provide a key to a number of …

Module theory over commutative asociative rings is usually extended to noncommutative
associative rings by introducing the category of left (or right) modules. An alternative to this …

We define non-unital exchange rings and we prove that ifIis an ideal of a ringR, thenRis an
exchange ring if and only ifIandR/Iare exchange rings and idempotents can be lifted …

A ring R is said to be clean if every element of R is a sum of an idempotent and a unit. The
class of clean rings is quite large and includes, for instance, semiperfect rings (and thus …