BL代数滤子公开问题的进一步求解（英文）  

Further solution to open problems of filters in BL-algebras

作　　者：王伟 杨鹏煕[1] 徐扬 Wang Wei;Yang Pengxi;Xu Yang(College of Sciences,Xi ' an Shiyou University,Xi'an 710065,China;National-Local Joint Engineering Laboratory of System Credibility Automatic Verification,Southwest Jiaotong University,Chengdu 610031,China;System Credibility Automatic Verification Engineering Lab of Sichuan Province,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西安石油大学理学院应用数学系,陕西西安710065 [2]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,四川成都610031 [3]西南交通大学四川省系统可靠性自动证明工程实验室,四川成都610031

出　　处：《纯粹数学与应用数学》2019年第2期208-214,共7页Pure and Applied Mathematics

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)

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?"

关 键 词：滤子 normal滤子 fantastic滤子 BL代数 

分 类 号：O153.1[理学—数学]