In this paper,a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed.The classes of this complete congruence which are intervals are discussed and their least and...In this paper,a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed.The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.展开更多
In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a de...In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a decomposable MS-algebra L can be uniquely determined by a congruence pair(θ_(1),θ_(2)),whereθ_(1)is a congruence on the de Morgan subalgebra L^(∞)of L andθ_(2)is a lattice congruence on the sublattice D(L)of L.They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L.Moreover,they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.展开更多
In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices...In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.展开更多
In this paper, we generalize Clifford semirings to left Clifford semirings bymeans of the so-called band semirings. We also discuss a special case of this kind of semirings,that is, strong distributive lattices of lef...In this paper, we generalize Clifford semirings to left Clifford semirings bymeans of the so-called band semirings. We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.展开更多
An algeber L is said to be simple, if its congruence lattice Con L reduces to the 2-elementchain {ω,v}. This paper describes the structure of finite simple Ockham algebras.
基金Foundation item： the National Natural Science Foundation of China （No. 10571061） the Science Foundation of Guangdong Province （No. 0501332） and the Science Foundation of the Department of Education of Yunnan Province （No. 07C10110）.
文摘In this paper,a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed.The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.
基金supported by 2nd International Conference for Mathematics,Statistics and Information Technology(ICMSIT for short)that held in the Faculty of ScienceTanta UniversityEgypt,18-20December,2018。
文摘In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a decomposable MS-algebra L can be uniquely determined by a congruence pair(θ_(1),θ_(2)),whereθ_(1)is a congruence on the de Morgan subalgebra L^(∞)of L andθ_(2)is a lattice congruence on the sublattice D(L)of L.They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L.Moreover,they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.
基金the Grants of Natural Scientific Foundation of China(Nos.61572013 and 61272196).
文摘In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are introduced.Then we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and inversesemigroups.As an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing operators.Consequently,a necessary and sufficient condition for theseoperators to be 69-condensing operators is given.Some further results on condensesemigroups considered by Chen et al.(Acta Math.Hung.119:281-305,2008)arediscussed and obtained in this paper.
文摘In this paper, we generalize Clifford semirings to left Clifford semirings bymeans of the so-called band semirings. We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.
文摘An algeber L is said to be simple, if its congruence lattice Con L reduces to the 2-elementchain {ω,v}. This paper describes the structure of finite simple Ockham algebras.
