In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean ordered subsemigroups are given by som...In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals of S. Furthermore, some characterizations for an ordered semigroup S to be a chain of archimedean ordered subsemigroups are also given by means of fuzzy subsets of S. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup S is a chain of archimedean ordered subsemigroups if and only if S is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of S form a chain.展开更多
In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In...In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1096101411271040)+4 种基金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)
文摘In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals of S. Furthermore, some characterizations for an ordered semigroup S to be a chain of archimedean ordered subsemigroups are also given by means of fuzzy subsets of S. In particular, by using the fuzzy prime radical theorem of ordered semigroups, we prove that an ordered semigroup S is a chain of archimedean ordered subsemigroups if and only if S is a semilattice of archimedean ordered subsemigroups and all weakly completely prime fuzzy ideals of S form a chain.
基金The NSF (10961014) of Chinathe NSF (S2011010003681) of Guangdong Province+3 种基金the Science and Technology Projects (2010B010600039) of Guangdong Provincethe Excellent Youth Talent Foundation (2012SQRL115ZD) of Anhui Provincethe University Natural Science Project (KJ2012B133) of Anhui Provincethe NSF (2007LZ01) of Fuyang Normal College
文摘In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.
