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.