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 …

For K a field, a Wedderburn K-linear category is a K-linear category A whose radical R is
locally nilpotent and such that A» 4 A/R is semi-simple and remains so after any extension of …

A recurring theme in a traditional introductory graduate algebra course is the existence and
consequences of relationships between different algebraic structures. This is also the theme …

By using theT2-orbit category of the derived category of a hereditary algebra, which is
proved to be a triangulated category too, we give a complete realization of a simple Lie …

These notes present an introduction into the spectrum of the category of modules over a
ring. We discuss the general theory of pure-injective modules and concentrate on the …

The significance of the canonical algebras for finite dimensional representation theory in
general is pointed out in Ringel's recent survey [22, section 1.5]. Canonical algebras and the …

We characterise those concealed-canonical algebras which arise as endomorphism rings of
tilting modules, all of whose indecomposable summands have strictly positive rank, as those …

arXiv:math/0604361v2 [math.AG] 3 Jul 2006 Homological Mirror Symmetry and Simple Elliptic
Singularities Page 1 arXiv:math/0604361v2 [math.AG] 3 Jul 2006 Homological Mirror Symmetry …

Rings which, from the ring-theoretic point of view, are very different may well have
categories of modules which are extremely similar. More generally, the category of modules …

In recent work, generalized persistence modules have proved useful in distinguishing noise
from the legitimate topological features of a data set. Algebraically, generalized persistence …