Localisations of rings in representation theory I and II

Abstract: Ring epimorphisms are important from a representation-theoretical point of view as they provide a way to compare categories of modules. In these talks we will use localisation techniques to characterise some classes of ring epimorphisms. The first talk will focus on torsion-theoretical localisations, after Gabriel, and their relation with flat ring epimorphisms. In the second talk we will discuss universal localisations, after Cohn and Schofield, and a generalised version due to Krause. These localisations will be useful to describe certain homological ring epimorphisms.