PUB - Publikationen an der Universität Bielefeld

Let Lambda be a finite-dimensional k-algebra with k algebraically closed. Bongartz has recently shown that the existence of an indecomposable. Lambda-module of length n > 1 implies that also indecomposable Lambda-modules of length n - 1 exist. Using a slight modification of his arguments, we strengthen the assertion as follows: If there is an indecomposable module of length n, then there is also an accessible one. Here, the accessible modules are defined inductively, as follows. First, the simple modules are accessible. Second, a module of length n >= 2 is accessible provided it is indecomposable and that there is a submodule or a factor module of length n - 1 which is accessible.