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
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
The inclusion ideal graph In(S)of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I,J are adjacent if and only if either I⊂J or J⊂I.The p...The inclusion ideal graph In(S)of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I,J are adjacent if and only if either I⊂J or J⊂I.The purpose of this paper is to study algebraic properties of the semigroup S as well as graph theoretic properties of In(S).We investigate the connectedness of In(S)and show that the diameter of In(S)is at most 3 if it is connected.We also obtain a necessary and sufficient condition of S such that the clique number of In(S)is the number of minimal left ideals of S.Further,various graph invariants of In(S),viz.perfectness,planarity,girth,etc.,are discussed.For a completely simple semigroup S,we investigate properties of In(S)including its independence number and matching number.Finally,we obtain the automorphism group of In(S).展开更多
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 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.
文摘The inclusion ideal graph In(S)of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I,J are adjacent if and only if either I⊂J or J⊂I.The purpose of this paper is to study algebraic properties of the semigroup S as well as graph theoretic properties of In(S).We investigate the connectedness of In(S)and show that the diameter of In(S)is at most 3 if it is connected.We also obtain a necessary and sufficient condition of S such that the clique number of In(S)is the number of minimal left ideals of S.Further,various graph invariants of In(S),viz.perfectness,planarity,girth,etc.,are discussed.For a completely simple semigroup S,we investigate properties of In(S)including its independence number and matching number.Finally,we obtain the automorphism group of In(S).
