We provide an affirmative answer for the question raised almost twenty years ago concerning the characterization of tilted artin algebras by the existence of a sincere finitely generated module which is not the middle of a short chain

Abstract. We describe the structure of semi-regular Auslander-Reiten components of artin algebras without external short paths in the module category. As an application we give a complete description of self-injective artin algebras whose Auslander-Reiten quiver admits a regular acyclic component without external short paths.

We prove that the component quiver ΣA of a connected self-injective artin algebra A of infinite representation type is fully cyclic, that is, every finite set of components of the Auslander-Reiten quiver ΓA of A lies on a common oriented cycle in ΣA.

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We investigate the categorical behaviour of morphisms between indecomposable projective modules over a special biserial algebra A over an algebraically closed field, which are associated to arrows of the Gabriel quiver of A.