弱交既约元的性质

Some properties of the weak meet irreducible element

首先引入弱上邻、弱交既约元的概念,其次利用弱上邻、上邻给出了弱交既约元、弱完全交既约元、弱连续交既约元的等价刻画,最后给出了分配的定向完备格上弱连续交既约元的一些基本性质。

Firstly, the concept of the weak adjacent and the weak meet irreducible element arc introduced. In addition , the equivalent characterizations of the weak meet irreducible element, the weak completely meet irreducible element, and the weak continuous meet irreducible clement are given based on the weak adjacent and adjacent. Finally, some properties of the weak continuous meet irreducible element in the distributively directed com- pleted lattice are obtained.