The model-theoretic investigation of modules has led to ideas, techniques and results which
are of algebraic interest, irrespective of their model-theoretic significance. It is these aspects …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …

1. Introduction. 2. Proper classes of triangles and phantom maps. 3. The Steenrod and Freyd
category of a triangulated category. 4. Projectie objects, resolutions, and deried functors. 5 …

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 …

An additive category with direct limits is said to be locally finitely presented provided that the
full subcategory of finitely presented objects is skeletally small and every object is a direct …

\My purpose in these lectures is not to present new results, but rather to give a different
perspective on some older results as illustrations of the interplay between functorial ideas …

Krullâ•fiGabriel dimension and the modelâ•’theoretic complexity of the category of modules over
group rings of finite g Page 1 J. London Math. Soc. (2) 78 (2008) 125–142 Cо2008 London …

The aim here is to emphasise the topological and geometric structure that the Ziegler
spectrum carries and to illustrate how this structure may be used in the analysis of particular …

We calculate the Krull–Gabriel dimension of the category of modules over any domestic
string algebra, in particular showing that it is finite, thus confirming a conjecture of Schröer …

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 …