基于理想的半单序超半群

On Semisimple Ordered Hypersemigroups in Terms of Ideals

本文给出了序超半群上几类正则序超半群的等价刻画和半单偏序超半群的等价刻画,并研究了几类相关性质。本文的主要结论是:设(S,。,≤)为序超半群,f是S上的模糊子集,S为左拟正则的当且仅当f≤1°f°1°f,类似地我们给出右拟正则的刻画;S是半单的当且仅当f≤1°f°1°f°1。

In this paper, equivalent characterizations of the classes of regular, quasi-regular and left(resp. right) regular ordered hypersemigroups are obtained and the equivalent characterization theorems for semisimple ordered hypersemigroups are also given, several related properties are investigated. The main results in this paper are as followed: let(S,°,≤) be an ordered hypersemigroup, f a fuzzy subset of S. Then Sis left(resp. right) regular if and only if f≤1°f°1.f(resp. f≤f°1°f°1), and Sis a semisimple ordered hypersemigroup if and only if f≤1°f°1°f°1.