浙江大学学报（理学版）2025，Vol.52Issue(3)：371-376,396,7.DOI:10.3785/j.issn.1008-9497.2025.03.009
剩余序半群的内部和闭包算子
Interior and closure operators on residuated ordered semigroup
摘要
Abstract
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Key words
residuated ordered semigroup/interior operator/closure operator/Galois adjoint pair/Heyting algebra分类
数学引用本文复制引用
李毅君,王军涛..剩余序半群的内部和闭包算子[J].浙江大学学报（理学版）,2025,52(3):371-376,396,7.基金项目
国家自然科学基金资助项目(12001423) （12001423）
教育部人文社会科学研究一般项目(24XJC72040001) （24XJC72040001）
陕西省自然科学基础研究计划项目(2024JC-YBMS-575) （2024JC-YBMS-575）
广东省哲学社会科学规划年度项目(GD23YGL17) （GD23YGL17）
陕西省教育厅青年创新团队科研项目(23JP132) （23JP132）
广东金融学院优秀青年博士科研启动项目(0000-KC20210050011570). （0000-KC20210050011570）
