Lefschetz properties of Gorenstein graded algebras associated to the Apéry set of a numerical semigroup

In this paper we study the Weak Lefschetz property of two classes of standard graded Artinian Gorenstein algebras associated in a natural way to the Apéry set of numerical semigroups. To this aim we also prove a general result about the transfer of the Weak Lefschetz property from an Artinian Gorenstein algebra to its quotients modulo a colon ideal.

Keywords

Lefschetz properties, graded rings, Artinian rings, Gorenstein rings, numerical semigroups

2010 Mathematics Subject Classification

13A30, 13E10, 13H10

Full Text (PDF format)

Received 1 February 2017

Received revised 17 July 2018

Accepted 7 August 2018

Published 3 May 2019