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 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
In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L<sub>i</sub> ∈ MS（i=1,2,...,n）then the Braided product of L<sub>i<...In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L<sub>i</sub> ∈ MS（i=1,2,...,n）then the Braided product of L<sub>i</sub>（i=1, 2,…,n） exists if and only if L<sub>1</sub>,...,L<sub>n</sub> have isomorphic skeletons.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 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
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+.
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In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that if L<sub>i</sub> ∈ MS（i=1,2,...,n）then the Braided product of L<sub>i</sub>（i=1, 2,…,n） exists if and only if L<sub>1</sub>,...,L<sub>n</sub> have isomorphic skeletons.
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 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.
