A class of Hilbert series and the strong Lefschetz property

Abstract

We determine the class of Hilbert series $\mathcal H$ so that if $M$ is a finitely generated zero-dimensional $R$-graded module with the strong Lefschetz property, then $M\otimes _k k[y]/(y^m)$ has the strong Lefschetz property for an indeterminate $y$ and all positive integers $m$ if and only if the Hilbert series of $M$ is in $\mathcal {H}$. Given two finite graded $R$-modules $M$ and $N$ with the strong Lefschetz property, we determine sufficient conditions in order that $M\otimes _kN$ has the strong Lefschetz property.