2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63692We demonstrate that, for CFT vertex operator algebras, C_2-cofiniteness and rationality is equivalent to regularity. In addition, we show that, for C_2-cofinite vertex operators algebras, irreducible weak modules are ordinary modules and C_2-cofinite, and V_L^+ are C_2-cofinite.latex, 15 pagesQuantum Algebratext