序半群Quantale完备化的进一步结果  

Some Further Results on Quantale Completions of Ordered Semigroups

作　　者：夏常春 赵彬[1] 韩胜伟[1] Chang Chun XIA;Bin ZHAO;Sheng Wei HAN(School of Mathematics and Information Science,Shaanxi Normal University,Xi＇an 710119,P.R.China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《数学学报（中文版）》2018年第5期811-822,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金重点项目(11531009);中央高校基本科研业务费专项资金项目(GK201501001)

摘　　要：本文给出了序半群上幂集Quantale的最大拓扑闭包的具体形式,即序半群的最小Quantale完备化.在此基础上,证明了Quantale范畴Quant是序半群范畴OSGrp^＊的满的反射子范畴.最后,给出了序半群Quantale完备化的一个应用.The main result of this paper is to give the concrete form of the largest topological closure of the power-set Quantale over an ordered semigroup. Based on which, it is proved that the category Quant of Quantale is a fully reflective subcategory of the category OSGrp^＊ of ordered semigroups. Finally, we give an application for the Quantale completions of ordered semigroups.

关 键 词：范畴 序半群 正则同余 拓扑闭包 Quantale完备化 

分 类 号：O153.1[理学—数学]