On the nilpotency index of the radical of a module category

Abstract

Let A be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to determine which vertices of QA are sufficient to be considered in order to compute the nilpotency index of the radical of the module category of A. Precisely, we study the above mentioned problem whenever A is a monomial or a toupie algebra where their Auslander-Reiten quivers are component with length. We also study the above problem for string algebras. We give concrete formulas to compute such index for many classes of algebras such as toupie algebras, tree algebras and some classes of pullback algebras over the hereditary algebras of type An, Dn and E6. Furthermore, we determine the index taking into account the ordinary quiver of the given algebras.