左R-模上Riesz空间的相关性质研究  

Study on some Properties of Riesz Spaces on left R-modules

作　　者：崔晓宇 周璞铉 汤建钢 孙锐娟 王金萌 刘晓芳 Cui Xiaoyu;Zhou Puxuan;Tang Jiangang;Sun Ruijuan;Wang Jinmeng;Liu Xiaofang(College of Mathematics and Statistics,Yili Normal University Yining,Xinjiang 835000,China;Institute of Applied Mathematics,Yili Normal University,Yining,Xinjiang 835000,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《伊犁师范大学学报（自然科学版）》2022年第4期1-7,共7页Journal of Yili Normal University：Natural Science Edition

基　　金：新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2019I024)。

摘　　要：基于ℓ-群、ℓ-环和线性空间上Riesz空间概念,在左R-模中引入格序结构,定义了左R-模上Riesz空间的概念,研究了左R-模上Riesz空间的基本性质,证明了涉及序理想、带、投影的特征定理.Based on the concepts of ℓ-groups, ℓ-rings and Riesz spaces on linear spaces, the lattice-ordered structure is introduced into left R-modules, the concept of Riesz spaces on left R-modules is defined, the basic properties of Riesz spaces on left R-modules are studied, and the characteristic theorems involving ordered ideals, bands and projections are proved.

关 键 词：左R-模上Riesz空间 正交 带 投影 

分 类 号：O154[理学—数学] O159[理学—基础数学]