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 first of a two-volume set that provides a modern account of the representation
theory of finite dimensional associative algebras over an algebraically closed field. The …

Modern developments in representation theory rely heavily on homological methods. This
book for advanced graduate students and researchers introduces these methods from their …

One of the main aims of this survey article is to show that the pure semisimplicity conjecture
(pss R) stated below has a positive solution for all rings R if and only if for any pair of division …

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms,
indecomposable finitely generated Gorenstein-projective A-modules. We prove that for a …

The idea of purity pervades human culture, from religion through sexual and moral codes,
cleansing rituals and dietary rules, to stratifications of societies into castes. It does so to an …

We uncover a connection between the model-theoretic notion of superstability and that of
noetherian rings and pure-semisimple rings. We characterize noetherian rings via …

Let C be a basic indecomposable hereditary K-coalgebra, where K is an arbitrary field. We
investigate a technique for studying C and left C-comodules by means of the left valued …

Let C be an indecomposable hereditary K-coalgebra, where K is an algebraically closed
field. We prove that every left C-comodule is a direct sum of finite dimensional C-comodules …

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 …