剩余序半群的内部和闭包算子  

Interior and closure operators on residuated ordered semigroup

作　　者：李毅君 王军涛 LI Yijun;WANG Juntao(School of Finance Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521,China;School of Science,Xi′an Shiyou University,Xi′an 710065,China)

机构地区：[1]广东金融学院金融数学与统计学院,广东广州510521 [2]西安石油大学理学院,陕西西安710065

出　　处：《浙江大学学报(理学版)》2025年第3期371-376,396,共7页Journal of Zhejiang University(Science Edition)

基　　金：国家自然科学基金资助项目(12001423);教育部人文社会科学研究一般项目(24XJC72040001);陕西省自然科学基础研究计划项目(2024JC-YBMS-575);广东省哲学社会科学规划年度项目(GD23YGL17);陕西省教育厅青年创新团队科研项目(23JP132);广东金融学院优秀青年博士科研启动项目(0000-KC20210050011570)。

摘　　要：通过引入剩余序半群的内部和闭包算子概念,研究了相关代数性质,讨论了剩余序半群内部和闭包算子之间的关系,得到了两者相互转化的方法。同时,讨论了剩余序半群内部和闭包算子集之间的关系,证明了两者之间可以建立伽罗瓦伴随对,给出了剩余序半群相关代数结构内部和闭包算子的刻画。In this paper,the concept of inner and closure operators on residuated ordered semigroups is introduced,some of their related algebraic properties are studied.Further the relationship between weak inner and strong closure operators on residuated ordered semigroups is explored,and a method for their mutual transformation is obtained.Meanwhile,the relationship between the set of internal operators and the set of closure operators on the residuated ordered semigroup is discussed,it is proved that a Galois adjoint pair can be established between this two sets.Finally,the characterization of internal and closure operators on some related algebraic structure of residuated ordered semigroup is given.

关 键 词：剩余序半群 内部算子 闭包算子 伽罗瓦伴随对 HEYTING代数 

分 类 号：O155[理学—数学]