On the composition factors of indecomposable modules in almost cyclic coherent Auslander-Reiten components

We prove that the indecomposable modules without selfextensions in generalized standard almost cyclic coherent Auslander-Reiten components without external short paths of artin algebra are uniquely determined by their composition factors. Moreover, we prove that there is a common bound on the numbers of indecomposable modules with the same composition factors lying in a generalized standard almost cyclic coherent Auslander-Reiten component without external short paths of artin algebra.