In this article, the authors describe the largest congruence induced by a kernel ideal of an MS-algebra and characterize those MS-algebras on which all the congruences are in a one-to-one correspondence with the kerne...In this article, the authors describe the largest congruence induced by a kernel ideal of an MS-algebra and characterize those MS-algebras on which all the congruences are in a one-to-one correspondence with the kernel ideals.展开更多
In this article, for any a in the MS-algebra L, the author considers the con- gruence of the form defined by （x,y） ∈θa→←x∧a°° = y ∧a° and x ∨ a°° = y ∨ a°°. A characterizat...In this article, for any a in the MS-algebra L, the author considers the con- gruence of the form defined by （x,y） ∈θa→←x∧a°° = y ∧a° and x ∨ a°° = y ∨ a°°. A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L ∈ K2 ∨ K3.展开更多
Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained ...Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.展开更多
The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties o...The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties of the space of all prime e-filters of an MS-algebra are observed. The concept of D-prime filters is introduced and then a set of equivalent conditions axe derived for a prime e-filter to become a D-prime filter in topological terms.展开更多
Here some properties on filters of double MS-algebras are descripted. We show that,for a normal filter F of a double MS-algebra (L;0, + )(x,y) ∈θ(F) (a,b ∈ F) (x ∧α)∨b+= (y ∧ a)∨ b+.
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
Here we show that there exists a greatest fixed point separating congruence denoted by ψ on a double MS-algebra (L;~0, +), Some properties of ψ under certain conditions on fixed point complete and fixed point distri...Here we show that there exists a greatest fixed point separating congruence denoted by ψ on a double MS-algebra (L;~0, +), Some properties of ψ under certain conditions on fixed point complete and fixed point distributive have also been described.展开更多
The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice ...The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice endomorphism on L with x≤x^(+)=x^(++)and the operations x→x°,x→x^(*)and x→x^(+)are linked by the identities x^(+*)=x^(*+)and x^(+)°=x°^(+).In this paper,we characterize congruences on a CPMS-algebra,and show that there are precisely eight non-isomorphic subdirectly irreducible nontrivial algebras in the class of these algebras and give a complete description of them.展开更多
An endomorphism on an algebra A is said to be strong if it is compatible with every congruence on A.If every congruence on A,other than the universal congruence,is the kernel of a strong endomorphism on A,then A is sa...An endomorphism on an algebra A is said to be strong if it is compatible with every congruence on A.If every congruence on A,other than the universal congruence,is the kernel of a strong endomorphism on A,then A is said to have the strong endomorphism kernel property.In this paper,we shall give a complete description of the structure of those symmetric extended MS-algebras that have this property via Priestley duality.展开更多
文摘In this article, the authors describe the largest congruence induced by a kernel ideal of an MS-algebra and characterize those MS-algebras on which all the congruences are in a one-to-one correspondence with the kernel ideals.
基金the Natural Science Foundation of Hubei Province
文摘In this article, for any a in the MS-algebra L, the author considers the con- gruence of the form defined by （x,y） ∈θa→←x∧a°° = y ∧a° and x ∨ a°° = y ∨ a°°. A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L ∈ K2 ∨ K3.
文摘Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.
文摘The notion of e-filters is introduced in an MS-algebra and characterized. The concept of D-filters is introduced and a set of equivalent conditions under which every D-filter is an e-filter are given. The properties of the space of all prime e-filters of an MS-algebra are observed. The concept of D-prime filters is introduced and then a set of equivalent conditions axe derived for a prime e-filter to become a D-prime filter in topological terms.
文摘Here some properties on filters of double MS-algebras are descripted. We show that,for a normal filter F of a double MS-algebra (L;0, + )(x,y) ∈θ(F) (a,b ∈ F) (x ∧α)∨b+= (y ∧ a)∨ b+.
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.
文摘Here we show that there exists a greatest fixed point separating congruence denoted by ψ on a double MS-algebra (L;~0, +), Some properties of ψ under certain conditions on fixed point complete and fixed point distributive have also been described.
文摘The variety CPMS of closure extended pseudocomplemented MS-algebras consists of the algebras(L;∧,∨,°,*,+,0,1)of type(2,2,1,1,1,0,0),where(L;∧,∨,°,*,+,0,1)is a pseudocomplemented MS-algebra,+is a lattice endomorphism on L with x≤x^(+)=x^(++)and the operations x→x°,x→x^(*)and x→x^(+)are linked by the identities x^(+*)=x^(*+)and x^(+)°=x°^(+).In this paper,we characterize congruences on a CPMS-algebra,and show that there are precisely eight non-isomorphic subdirectly irreducible nontrivial algebras in the class of these algebras and give a complete description of them.
文摘An endomorphism on an algebra A is said to be strong if it is compatible with every congruence on A.If every congruence on A,other than the universal congruence,is the kernel of a strong endomorphism on A,then A is said to have the strong endomorphism kernel property.In this paper,we shall give a complete description of the structure of those symmetric extended MS-algebras that have this property via Priestley duality.
