双重半伪补de Morgan-代数滤子同余关系的注记  

A Note on the FilterCongruence of de Morgan Algebraswith Double Demi-Pseudocomplementation

作　　者：赵秀兰[1] 史永杰[2] Zhao Xiulan;Shi Yongjie(Department of Mathematics and Physics,Huanghe Srcience and Technology College,Zhengzhou City,He Nan Protince 450063;School of Mathematics,Shantou Lniversity,Shantou City,Guangdong Prorince 515063)

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：《黄河科技学院学报》2020年第11期96-100,共5页Journal of Huanghe S&T College

基　　金：国家自然科学基金项目(11701355)。

摘　　要：双重半伪补de Morgan代数是将双重半伪补代数类与de Morgan代数类相结合而形成的一个新的代数类,是一个有界分配格上赋予三个一元运算:双重半伪补运算与de Morgan运算。对双重半伪补de Morgan代数的滤子同余关系作进一步的研究:首先,基于双重半伪补de Morgan代数的运算规律以及双重半伪补运算与de Morgan运算的关联性,论证了双重半伪补de Morgan代数正则p-滤子同余关系的保序性以及同余置换性,根据双重半伪补de Morgan代数所体现的运算属性,论证了正则p-滤子格对格的二元运算是封闭的,获得了正则p-滤子格是滤子格的子格的结论。其次,在格与序代数理论中,涉及滤子,必然伴随着滤子同余关系,同余关系是保持运算的等价关系。借助于双重半伪补de Morgan代数的正则p-滤子同余关系,论证了正则p-滤子与正则p-滤子同余关系是同构的。所得结论为其他分配格代数类正则滤子性质的研究提供了方法,同时,为研究多元运算代数类结构提供理论支持。De Morgan algebra with double demi-pseudocomplementationis a new kind of algebra which combines double demi-pseudocomplementation withde Morgan algebra.It is a bounded distributive lattice which is endowed with three unary operations.Based on the operations of de Morgan algebra with double demi-pseudocomplementation and the correlation between the double demi-pseudocomplement and the de Morganoperation.This paper further studied the filter congruence of de Morgan algebras with double demi-pseudocomplementation.First of all,based on the operation law of the de Morgan algebra with double demi-pseudocomplementation and the correlation between the double demi-pseudocomplementation and the de Morgan operation,the order preserving and the congruence permutation of the regular p-filter congruence relation of the de Morgan algebra with double demi-pseudocomplementation are proved.According to the operation attribute of the de Morgan algebra with double demi-pseudocomplementationgeneration,it is proved that the binary operation of regular p-filter lattices on lattices is closed,and the conclusion that regular p-filter lattices are sublattices of filter lattices is obtained.Secondly,in the theory of lattice and ordered algebra,when it comes to filter,it must be accompanied by filter congruence,which is to keep the equivalence of operation.By means of the regular p-filter congruence relation of de Morgan algebras with double demi-pseudocomplementation,it is proved that the regular p-filter congruence relation and the regular p-filter congruence relation are isomorphic.The results provide a method for studying the regular filter properties of other distributive Lattice algebras and theoretical support for studying the class structure of multivariate operation algebras.

关 键 词：半伪补代数 双重半伪补代数 双重半伪补de Morgan代数 滤子 同余关系 

分 类 号：O153.1[理学—数学]