PUB - Publikationen an der Universität Bielefeld

Algebraically compact modules play an important role in representation theory. They have been introduced both by logicians and by algebraists as the basic class of representations of any ring. We will concentrate on algebraically compact modules which are related to tubes in the Auslander-Reiten quiver of an artin algebra. We are going to survey part of the present knowledge and typical examples. The decomposition results are similar to those known for algebraically compact abelian groups, whereas some of the embedding properties of the relevant categories provide completely different features.