关于半格的几个结果(英文)  

Some Results on Semilattice

作　　者：朱玉山[1] 

机构地区：[1]中国计量学院理学院数学系,浙江杭州310018

出　　处：《山西师范大学学报（自然科学版）》2006年第3期8-12,共5页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：一个半格可以定义为一个泛代数,也可以定义为一个偏序集.本文中,我们证明了作为泛代数的半格的定义与作为偏序集的半格的定义是等价的.为了刻划半格的两种不同定义间的关系,我们建立了两个等式.此外,我们建立了一个充分必要条件.这一充分必要条件反映了两个半格之间的同构与这两个半格的理想格之间的关系.A semilattice can be defined as a universal algebra, and it can also be defined as a partial ordered set. In this paper, we proved that the definition of a semilattice as a universal algebra and the definition of a semilattice as a partial ordered set are equivalent. In order to describe the relationship between two kinds of definitions for a semilattice, we established two formulas. Moreover, we proved a necessary and sufl%ient condition showing the relationship between the isomorphisms of semilattices and the isomorphisms of the lattices of the ideals of the semilattices.

关 键 词：半格 理想 等价 同构 

分 类 号：O153.5[理学—数学]