The weak Lefschetz property of a special class of Artinian algebras over fields of positive characteristic

TL;DR

This paper investigates how the weak Lefschetz property of certain Artinian algebras, defined by monomial ideals, varies with the characteristic of the base field, revealing characteristic-dependent behaviors.

Contribution

It provides new insights into the characteristic dependence of the weak Lefschetz property for a specific class of monomial ideals in polynomial rings.

Findings

Weak Lefschetz property depends on the characteristic of the field.

Identification of conditions under which the property holds or fails.

Analysis of monomial ideals in positive characteristic fields.

Abstract

In this paper, we study the dependence of the weak Lefschetz property of algebras defined by a special class of monomials ideals in a polynomial ring with coefficient in a field, to the characteristic of the base field.