Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on com...Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.展开更多
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, 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...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.展开更多
A semigroup is called completely J（e）-simple if it is isomorphic to some Rees matrix semi- group over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellat...A semigroup is called completely J（e）-simple if it is isomorphic to some Rees matrix semi- group over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J（e）-simple semigroups form a quasivarity. Moreover, the construction of free completely J（e）simple semigroups is given. It is found that a free completely J（e）-simple semigroup is just a free completely J＊-simple semigroup and also a full subsemigroup of some completely simple semigroups.展开更多
We consider particular compatible orders on a given completely simple semi- group Sx= M（（x）; I, A; P） where （x） is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace ...We consider particular compatible orders on a given completely simple semi- group Sx= M（（x）; I, A; P） where （x） is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.展开更多
基金National Natural Science Foundation of China(No.11671056)General Science Foundation of Shanghai Normal University,China(No.KF201840)。
文摘Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.
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Supported by the National Natural Science Foundation of China (Grant No. 10961014)the Science and Technology Projects in Guangdong Province (Grant No. 2010B010600039)+3 种基金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, 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.
基金Supported by National Natural Science Foundation of China(Grant No.11361027)the Natural Science Foundation of Jiangxi Provincethe Science Foundation of the Education Department of Jiangxi Province,China
文摘A semigroup is called completely J（e）-simple if it is isomorphic to some Rees matrix semi- group over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J（e）-simple semigroups form a quasivarity. Moreover, the construction of free completely J（e）simple semigroups is given. It is found that a free completely J（e）-simple semigroup is just a free completely J＊-simple semigroup and also a full subsemigroup of some completely simple semigroups.
文摘We consider particular compatible orders on a given completely simple semi- group Sx= M（（x）; I, A; P） where （x） is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.
基金supported by NSFC(No.10971160,No.11226044)Shaanxi Provincial Education Department Fund(No.12JK0876)the Young Science and Technology Fund of Xi'an University of Architecture and Technology(No.QN1136)
