Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through finite posets. We also study finite distributive nearlattices through the concepts of dual atoms, boolean elements, complemented elements and irreducible elements. We prove that the sets of boolean elements and complemented elements form semi-boolean algebras. We show that the set of boolean elements of a finite distributive lattice is a boolean lattice.

中文翻译：

---

有限分布近格

我们的主要目标是通过某些有序结构开发有限分布近格的表示。这种表示通过有限偏集对由 Birkhoff 给出的众所周知的有限分布格子的表示进行了概括。我们还通过对偶原子、布尔元素、互补元素和不可约元素的概念来研究有限分布近晶格。我们证明布尔元素和补充元素的集合形成半布尔代数。我们证明了有限分布格的布尔元素集是一个布尔格。