Some algebraically compact modules. I

Claus Michael Ringel

Abstract. Given a finite dimensional monomial algebra, one knows that
some finite dimensional indecomposable modules may be described by
words (finite sequences of letters) using as letters the arrows of the
quiver and their formal inverses. To every word w, one can attach a
so-called string module M(w). Here, we are going to construct certain
infinite dimensional modules: We will consider N-words and Z-words
(thus infinite sequences of letters) satisfying suitable periodicity
conditions. To every such N-word or Z-word x, we describe an algebraically
compact module C(x). This module C(x) is obtained from the corresponding
string module M(x) as a kind of completion.