BL代数滤子公开问题的进一步求解（英文）

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英文篇名：Further solution to open problems of filters in BL-algebras 作者：王伟 ; 杨鹏煕 ; 徐扬 英文作者：Wang Wei;Yang Pengxi;Xu Yang;College of Sciences, Xi′an Shiyou University;National-Local Joint Engineering Laboratory of System Credibility Automatic Verification,Southwest Jiaotong University;System Credibility Automatic Verification Engineering Lab of Sichuan Province,Southwest Jiaotong University; 关键词：滤子 ; normal滤子 ; fantastic滤子 ; BL代数 英文关键词：filter;;normal filter;;fantastic filter;;BL-algebras 中文刊名：CCSX 英文刊名：Pure and Applied Mathematics 机构：西安石油大学理学院应用数学系;西南交通大学系统可靠性自动证明国家地方联合工程实验室;西南交通大学四川省系统可靠性自动证明工程实验室; 出版日期：2019-06-25 出版单位：纯粹数学与应用数学 年：2019 期：v.35 基金：国家自然科学基金(11571281,61673320);; 国家空间动力重点实验室基础项目(202300006);; 中央大学基础研究基金(2682017ZT12);; 陕西省大学生创新创业训练计划资助项目(201819062) 语种：英文; 页：CCSX201902009 页数：7 CN：02 ISSN：61-1240/O1 分类号：86-92

摘要

基于之前的工作,进一步刻画了BL代数的fantastic和normal滤子的等价条件,得到了两种滤子之间的条件等价关系,全面地解决了关于这两种滤子之间关系的两个公开问题:"在什么样的合适条件下,一个normal滤子成为一个fantastic滤子?"和"在什么合适的条件下, normal滤子的拓展性成立?"
        Based on our previous work, we further characterize the fantastic filter and normal filter in BL-algebras, then get the conditional equivalent relation between the two filters, and completely solving two open problems regarding the relationship between these two filters of BL-algebras:(1) "Under what suitable condition a normal filter becomes a fantastic filter?" and(2) "(Extension property for a normal filter) Under what suitable condition extension property for normal filter holds?"

引文

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