In this survey article we describe some geometric results in the theory of noncommutative
rings and, more generally, in the theory of abelian categories. Roughly speaking and by …

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 …

This is the second revised edition of an introduction to contemporary relative homological
algebra. It supplies important material essential to understand topics in algebra, algebraic …

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

The first two chapters of this book offer a modern, self-contained exposition of the
elementary theory of triangulated categories and their quotients. The simple, elegant …

The language of Mathematics has changed drastically since the middle of the twentieth
century, in particular after Grothendieck's ideas spread from algebraic geometry to many …

The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed
account of what should be known by everybody working in, or using, category theory. As …

Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …

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

We give a sufficient condition for an Ext-finite triangulated category to be saturated.
Saturatedness means that every contravariant cohomological functor of finite type to vector …