基于理想的半单序超半群  

On Semisimple Ordered Hypersemigroups in Terms of Ideals

作　　者：谢祥云[1] 高连飞 李敏 XIE Xiang-yun;GAO Lian-fei;LI Min(School of Mathematics and Computational Science,Wuyi University,Jiangmen 529020,China)

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《模糊系统与数学》2020年第1期9-18,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11361027,11271040);广东省自然科学基金资助项目(2014A030313625,2018A030313063);研究生示范课建设项目(2016SFKS_40)。

摘　　要：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.

关 键 词：序超半群 半单 理想 模糊理想 

分 类 号：O152[理学—数学]