Abstract In this article, we study the weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, proving that several results known in the Artinian case hold also in this more general setting. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements.

中文翻译：

---

Lefschetz 属性和超平面排列

摘要 在本文中，我们研究了弱和强 Lefschetz 性质，以及几乎 revlex 理想的相关概念，在非阿蒂尼亚情况下，证明在阿蒂尼亚情况下已知的几个结果在这个更一般的情况下也成立。然后我们将获得的结果应用于研究超平面排列的雅可比代数。