2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134601The authors T.Harima, J.C.Migliore, U.Nagel and J.Watanabe characterized the Hilbert function of algbebras with the Lefschetz property. We extend this characterization to algebras with the Lefschetz property m times. We also give upper bounds for the Betti numbers of Artinian algebras with a given Hilbert function and with the Lefschetz property m times and describe the cases in which these bounds are reached.19 pagesCommutative Algebra13F20 (Primary), 13E10 (Secondary)text