双重半伪补MS代数的正则滤子  

Normal Filter on MS-algebras with Double Demi-Pseudocomplementation

作　　者：赵秀兰[1] 史永杰[2] ZHAO Xiu-lan;SHI Yong-jie(Department of Mathematics and Physics,Huang He Science and Technology College,Zhengzhou 450063,China;School of Mathematics,Shantou University,Shantou 515063,China)

机构地区：[1]黄河科技学院数理部,河南郑州450063 [2]汕头大学理学院,广东汕头515063

出　　处：《数学的实践与认识》2020年第13期202-208,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11701355)。

摘　　要：正则滤子是刻画代数结构的工具,借助正则滤子同余关系有助于了解代数的内部结构.首先在双重半伪补MS代数上,引入正则滤子的概念,结合双重半伪补MS代数的运算属性,构造出具有正则滤子的最大同余关系;其次,利用双重半伪补MS代数具有正则滤子最小同余关系表达式,给出了具有正则滤子的最小同余关系与最大同余关系的等式关系.所得结论为其它分配格代数类正则滤子性质的研究提供了方法,丰富了分配格理论,为进一步研究分配格代数类的代数结构提供理论支持.Normal filter is a tool for describing the structure of algebra.With the help of the congruence relation of normal filter,it is helpful to understand the internal structure of algebra.Firstly,the concept of normal filter is introduced on MS-algebras with double demi-pseudocomplementation,and the maximum congruence relation with normal filter is constructed by combining the operation properties of MS-algebras with double demipseudocomplementation.Secondly,the expression of minimum congruence relation with normal filter is given by using the expression of minimum congruence relation with normal filter on MS-algebras with double demi-pseudocomplementation.The conclusion provides a method for the study of the normal filter properties of other distributive lattice algebral,enriches the theory of distributive lattice and provides theoretical support for further study of the algebraic structure of the class of distributive algebra.

关 键 词：半伪补代数 双重半伪补代数 双重半伪补MS代数 滤子 正则滤子 同余关系 

分 类 号：O153[理学—数学]