Stratifying systems over hereditary algebras

This paper deals with stratifying systems over hereditary algebras. In the case of tame hereditary algebras we obtain a bound for the size of the stratifying systems composed only by regular modules and we conclude that stratifying systems cannot be complete. For wild hereditary algebras, with more than two vertices, we show that there exists a complete stratifying system whose elements are regular modules. In any other case, we conclude that there are no stratifying system consisting of regular modules.