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Filter topologies on MV-algebras

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讲座题目:Filter topologies on MV-algebras
讲座人: 杨义川教授
讲座时间:19:00
讲座日期:2020-11-12
地点:腾讯会议(407737002)

报告内容简介:In this talk, we will first explain the reason that filter topological characterization of abelian l-groups cannot be easily translated into MV-algebras. Then,for a 2-divisible MV-algebra A, we prove that A is semi-simple iff it is Hausdorff with respect to any filter topology induced by a lattice filter, which is generated by an exceeding zero element. After that, for an arbitrary MV-algebra A, we prove that A is semi-simple iff for any lattice filter F which does not intersect any proper MV-ideal, A is Hausdorff with respect to F. Then, we give several equivalent characterizations for a filter topology making an MV-algebra into a topological MV-algebra. Finally, an MV-chain with a filter topology is shown to be a topological MV-algebra, and a structure theorem of MV-algebras with Hausdorff compact filter topologies is given. (This talk contains several related works cooperated with Wei Luan, Hans Weber, and Xueting Zhao)

报告人简介:杨义川,北京航空航天大学大学教授,负责的《理科高等代数》获国家级首批一流课程认定。曾获国家教学成果二等奖、北京市教学成果特等奖,教育部基础学科拔尖人才优秀导师奖、宝钢优秀教师奖、北京市教学名师奖等。任Soft Computing编委(Area Editor)、《高等数学研究》编委,教育数学专委会副秘书长,中国工业与应用数学学会常务理事,教育部大学数学教学指导委员会委员。

 
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