2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223026Let A be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group G. Here we study a growth function related to the graded polynomial identities satisfied by A by computing the exponential rate of growth of the sequence of graded codimensions of A. We prove that the G-exponent of A exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of A.Rings and Algebras16R10, 16W50, 16P90text