Hilbert Function and Betti Numbers of Algebras with Lefschetz Property of Order m

The authors in Harima et al. (2003 Harima , T. , Migliore , J. C. , Nagel , U. , Watanabe , J. ( 2003 ). The weak and strong Lefschetz properties for artinian K-algebras . Journal of Algebra 262 : 99 – 126 .Crossref], Web of Science ®] , Google Scholar]) characterize the Hilbert function of algebras 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.