In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.展开更多
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, qu...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.展开更多
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.
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)+1 种基金the Natural Science Foundation of Guangdong Province(Grant No.2014A030313625)the Key Project of Department of Education of Guangdong Province(Grant No.2014KZDXM055)
文摘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.
