■-分配偏序集

■-distributive Posets

引入了■-分配偏序集的概念并对其一些性质进行讨论,特别地,证明了:(1)偏序集P是■-分配的当且仅当由P中所有有限集生成的cut构成的集族也是■-分配的;(2)偏序集P是强代数的当且仅当P是预代数和■-分配的当且仅当P是严格无限分配和广义强代数的。

In this paper,the concept of ■-distributive posets is introduced.Some properties of ■-distributive posetss are investigated.Several characterizations of ■-distributive posets are obtained.Especially,it is proved that(1)A poset P is ■-distributive iff the set consists of all finitely generated cuts of P is ■-distributive.(2)A poset P is strongly algebraic iff P is prealgebraic and^distributive iff P is strictly infinitely and generalized strongly algebraic.