Some Characterizations of Chains of Archimedean Ordered Semigroups

DOI：10.3770/j.issn:2095-2651.2013.02.009

 作者 单位 唐剑 阜阳师范学院数学与计算科学学院，安徽 阜阳 236037 谢祥云 五邑大学数学与计算科学学院，广东 江门 529020

本文首先引入了一个序半群\$S\$的准素模糊理想的概念,通过序半群\$S\$上的一些二元关系以及它的理想的模糊根给出了该序半群是阿基米德序子半群的半格的一些刻画.进一步地借助于序半群\$S\$的模糊子集对该序半群是阿基米德序子半群的半格进行了刻画.尤其是通过序半群的模糊素根定理证明了序半群\$S\$是阿基米德序子半群的链当且仅当\$S\$是阿基米德序子半群的半格且\$S\$的所有弱完全素模糊理想关于模糊集的包含关系构成链.

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup \$S\$ to be a semilattice of archimedean ordered subsemigroups are given by some binary relations on \$S\$ and the fuzzy radical of fuzzy ideals of \$S\$. Furthermore, some characterizations for an ordered semigroup \$S\$ to be a chain of archimedean ordered subsemigroups are also given by means of fuzzy subsets of \$S\$. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup \$S\$ is a chain of archimedean ordered subsemigroups if and only if \$S\$ is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of \$S\$ form a chain.