2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77164We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu's $C_{2}$-finiteness condition holds, fusion rules are finite and the vertex operator algebras themselves are finitely generated.17 pages, Latex; to appear in J. of AlgQuantum Algebratext