The central aim of this book is to understand modules and the categories they form through
associated structures and dimensions, which reflect the complexity of these, and similar …

This book surveys more than 125 years of aspects of associative algebras, especially ring
and module theory. It is the first to probe so extensively such a wealth of historical …

We study Mittag-Leffler conditions on modules providing relative versions of classical results
by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we …

Let R be a left pure-semisimple ring. It is proved that if R has self-duality or if R is a
polynomial identity ring, then R is of finite representation type. If there exists an example of a …

Ž. We recall that a ring R with identity is said to be of finite representation type if it is right
artinian and has only finitely many isomorphism Ž. Ž classes of finitely generated …

Ž. It is well known that pure-injective s algebraically compact modules behave well in
relation to direct sum decompositions. Any indecomposable wx pure-injective module has …

We investigate (existence of) Auslander–Reiten triangles in a triangulated category in
connection with torsion pairs, existence of Serre functors, representability of homological …

Let R be a hereditary, indecomposable, left pure semisimple ring. Inspired by [I. Reiten, CM
Ringel, Infinite dimensional representations of canonical algebras, Canad. J. Math. 58 …

Let R be a right pure semisimple ring, ie, a ring R such that every right R-module is a direct
sum of finitely generated modules. It is proved that R is of finite representation type if and …

Let R be a left artinian ring such that every finitely presented right. ft-module is of finite
endolength. It is shown that the cardinality of the set of isomorphism classes of preinjective …