On Fuzzy Quasi-Ideals of Ordered Semigroups  

作　　者：Jian TANG Xiangyun XIE 

机构地区：[1]School of Mathematics and Computational Science, Fuyang Normal College, Anhui 236037, P. R. China [2]School of Mathematics and Computational Science, Wuyi University, Guangdong 529020, P. R. China

出　　处：《Journal of Mathematical Research with Applications》2012年第5期589-598,共10页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10961014);the Science and Technology Projects in Guangdong Province (Grant No. 2010B010600039);the Guangdong Provincial Natural Science Foundation of China (Grant No. S2011010003681);the Anhui Provincial Excellent Youth Talent Foundation (Grant No. 2012SQRL115ZD);the University Natural Science Project of Anhui Province (Grant No. KJ2012B133);the Fuyang Normal College Natural Science Foundation (Grant No. 2007LZ01)

摘　　要：In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.

关 键 词：fuzzy quasi-ideal completely semiprime fuzzy quasi-ideal strongly regular ordered semigroup left simple ordered semigroup right simple ordered semigroup. 

分 类 号：O153.3[理学—数学] O152.7[理学—基础数学]