A Note on a Conjecture Regarding the Weak Lefschetz Property of a Special Class of Artinian Algebras

Abstract

Let $$R = K[x_1,\ldots ,x_r]$$ be the polynomial ring over an infinite field K. For a class of Artinian K-algebras $$A = R/I$$ , where I is a monomial ideal of certain specific form and K has some positive characteristics, we examine the weak Lefschetz property of A for various choices of I. In particular, these results support parts of a conjecture by Migliore, Miro-Roig and Nagel in some positive characteristics, and reveal that another part of their conjecture is characteristic-dependent.