An Investigation on Left Hyperideals of Ordered Semihypergroups  

作　　者：Jian TANG Xiangyun XIE 

机构地区：[1]School of Mathematics and Statistics, Fuyang Normal University [2]School of Mathematics and Computational Science, Wuyi University

出　　处：《Journal of Mathematical Research with Applications》2017年第4期419-434,共16页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11361027);the University Natural Science Project of Anhui Province(Grant No.KJ2015A161);the Natural Science Foundation of Guangdong Province(Grant No.2014A030313625);the Key Project of Department of Education of Guangdong Province(Grant No.2014KZDXM055)

摘　　要：In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore,we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover, we give some characterizations of weakly quasiprime left hyperideals by the left hyperideals and weakly m-systems. We also characterize the quasi-prime left hyperideals in terms of the m-systems. In particular, we prove that an ordered semihypergroup S is strongly semisimple if and only if every left hyperideal of S is the intersection of all quasi-prime left hyperideals of S containing it.In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore,we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover, we give some characterizations of weakly quasiprime left hyperideals by the left hyperideals and weakly m-systems. We also characterize the quasi-prime left hyperideals in terms of the m-systems. In particular, we prove that an ordered semihypergroup S is strongly semisimple if and only if every left hyperideal of S is the intersection of all quasi-prime left hyperideals of S containing it.

关 键 词：ordered semihypergroup minimal left hyperideal maximal left hyperideal weakly prime left hyperideal quasi-prime left hyperideal weakly quasi-prime left hyperideal 

分 类 号：O153[理学—数学]