On the nilpotency index of the radical of a module category

CHAIO CLAUDIA, GUAZZELLI VICTORIA, PAMELA SUAREZ.

JOURNAL OF PURE AND APPLIED ALGEBRA

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2023 vol. 227

0022-4049

Let A be a finite dimensional representation-finite algebra overan algebraically closed field. The aim of this work is to determine which vertices of Q_A 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 A_n, D_n and E_6. Furthermore, we determine the index taking into account the ordinary quiver of the given algebras.