A Class of Hilbert Series and the Strong Lefschetz Property

TL;DR

This paper characterizes the Hilbert series classes ensuring the preservation of the strong Lefschetz property under tensor products of graded modules, providing new insights into algebraic structures with this property.

Contribution

It identifies the class of Hilbert series that guarantee the strong Lefschetz property is maintained under specific tensor product operations.

Findings

Characterizes Hilbert series classes for the strong Lefschetz property

Provides conditions for tensor products of modules to have the property

Establishes when the property is preserved under tensoring with k[y]/(y^m)

Abstract

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