EBL-代数上的蕴涵滤子与正蕴涵滤子  

Implicative Filters and Positive Implicative Filters in EBL-Algebras

作　　者：左卫兵 韩睿 ZUO Wei-bing;HAN Rui(College of Mathematics and Statistics,North China Universityof Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《兰州文理学院学报（自然科学版）》2022年第5期20-27,共8页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金项目(12071133)。

摘　　要：滤子理论在多值逻辑及其相关代数的研究中扮演着重要的角色.在EBL-代数上引入蕴涵滤子、正蕴涵滤子以及Boolean滤子等概念,研究它们的性质和相关的等价刻画,得到了正蕴涵滤子是蕴涵滤子、Boolean滤子和正蕴涵滤子等价的结论.通过滤子构建EBL-代数上的同余关系,并从商代数的角度证明了一些滤子的性质.The filter theory plays an important role in studying multiple-valued logic and the related algebras.The concepts of implicative filter,positive implicative filter and Boolean filter are introduced into EBL-algebras,and their properties and related equivalent characterizations are studied.Furthermore,the conclusions that the positive implicative filter is an implicative filter and the positive implicative filter is equivalent to the Boolean filter are obtained.At the same time,congruence relations in EBL-algebras are constructed through filters,and the properties of some filters are proved from the perspective of quotient algebras.

关 键 词：EBL-代数 Boolean滤子 蕴涵滤子 正蕴涵滤子 同余 

分 类 号：O153.1[理学—数学] O141.1[理学—基础数学]