双重伪补Ockham代数的理想与滤子的构造  

Ideal and Filter Construction of Double Pseudo-Complement Ockham Algebras

作　　者：赵秀兰[1] 刘洁[1] 马红娟[1] Zhao Xiulan;Liu jie;Ma Hongjuan(Engineering Department,Huanghe Science&Technology College,Zhengzhou City,Henan Province 450063)

机构地区：[1]黄河科技学院工学部,河南郑州450063

出　　处：《黄河科技学院学报》2024年第2期33-36,共4页Journal of Huanghe S&T College

基　　金：河南省科技厅软科学研究项目(232400411122);郑州市基础研究及应用基础研究专项项目(ZZSZX202111)。

摘　　要：序代数理论在理论计算机、多值逻辑学、信息系统科学等方面有着广泛且重要的应用。在序代数研究领域,理想和滤子是刻画代数结构的重要工具。双重伪补Ockham代数是在双重伪补代数和Ockham代数基础上定义的一类新的代数类,基于双重伪补Ockham代数的运算规律以及双重伪补运算与Ockham代数运算的关联性,对双重伪补Ockham代数的理想与滤子做进一步的研究。首先,运用Ockham代数的运算构造出双重伪补Ockham代数的滤子,并探讨了相关性质。其次,借助于双重伪补Ockham代数核理想和余核滤子的充要条件构造出了核理想和余核滤子的具体集合形式。所得结论为其他序代数类的理想和滤子性质的研究提供了方法,也将有助于进一步探索序代数理论在其他学科如模糊集、计算机科学中的应用。The theory of order algebra has been widely used in theoretical computer,multi-valued logic,information system science and so on.In the field of ordered algebra,ideal and filter are important tools to describe the structure of algebras.Double pseudo-complement Ockham algebras are a new class of algebras defined on the basis of double pseudo-complement algebras and Ockham algebras.Based on the operation rules of double pseudo-complement Ockham algebras and the correlation between double pseudo-complement Ockham algebras,the ideals and filters of double pseudo-complement Ockham algebras are further studied.Firstly,filters of double pseudo-complement Ockham algebras are constructed by the operation of Ockham algebras,and the related properties are discussed.Secondly,by means of sufficient and necessary conditions of double pseudo-complement Ockham algebraic kernel ideal and cokernel filter,the concrete set form of kernel ideal and cokernel filter is constructed.The results will provide a method for the study of the ideal and filter properties of other order algebras,and will be helpful to further explore the application of order algebra theory in other disciplines such as fuzzy sets and computer science.

关 键 词：伪补代数 双重伪补Ockham代数 理想 滤子 核理想 余核滤子 

分 类 号：O151[理学—数学]