基于区间集非交换剩余格广义正规滤子的广义商代数表示定理  

Representation Theorem of Generalized Quotient Algebra Based on Interval Set Non-commutative Remaining Lattice Generalized Normal Filter

作　　者：乔希民 刘晓民 吴洪博[3] QIAO Xi-min;LIU Xiao-min;WU Hong-bo(Department of Basic Education,Guangzhou College of Technology and Business,Foshan 510850,China;School of Mathematics and Computer Application,Shangluo College,Shangluo 726000,China;School of Mathematics and Information Science Shaanxi Normal University,Xi'an 710062,China)

机构地区：[1]广州工商学院基础教学部,广东佛山510850 [2]商洛学院数学与计算机应用学院,陕西商洛726000 [3]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《模糊系统与数学》2020年第6期150-156,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61572016);陕西省自然科学基础研究计划项目(2014JM1019)。

摘　　要：基于区间集思想和同余理论,引入区间集非交换剩余格的广义滤子及广义正规滤子的概念,讨论用区间集非交换剩余格的广义正规滤子构造一种广义同余关系,并用区间集上非交换剩余格的广义同余关系证明其所诱导的广义商代数构造一个区间集上非交换剩余格。Based on the idea of interval sets and congruence theory,the concepts of generalized filters and generalized regular filters for non-commutative residual lattices of interval sets are introduced,and the construction of a generalized congruence relationship with generalized regular filters of non-commutative residual lattices for interval sets is discussed.The generalized congruence relation of non-commutative residual lattices on interval sets proves that the generalized quotient algebra induced by it constructs a no-commutative residual lattice on interval sets.

关 键 词：区间集非交换剩余格 I(2^U)上广义等价关系 I(2^U)上广义同余关系 广义正规滤子 广义商代数 构造性方法 

分 类 号：O141[理学—数学]