ABSTRACT
Let k be an algebraically closed field, A be a finite-dimensional algebra over k,Γ a be the Auslander-Reiten quiver of A. In this paper we give a necessary and sufficient condition for a coherent component Γ of Γ a such that the translation quiver obtained from Γ by deleting the DTr-orbits of projectives is connected and has property that its DTr-orbits are finite.
