左R-模上Riesz空间范畴中内射对象的性质研究  

Study on some Properties of the Injective Objects in the Category of Riesz Spaces on Left R-modules

作　　者：周璞铉 汤建钢 Zhou Puxuan;Tang Jiangang(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）》2023年第4期1-9,共9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：基于左R-模上Riesz空间的相关性质的研究,给出左R-模上Riesz空间范畴中内射对象的概念,研究了左R-模上Riesz空间范畴中内射对象的可裂性,证明了一簇左R-模上Riesz空间的乘积是内射对象当且仅当簇内的每一个左R-模上Riesz空间是内射对象.Based on the Study that on some Properties of Riesz Spaces on Left R-modules,we gave the concept of injective objects in the Category of Riesz Spaces on Left R-modules,and studied the separability of injective objects in the category of Riesz spaces on left R-modules,a product of a bunch of Riesz Spaces on Left R-modules is an injective object if and only if every one is an injective object is proved.

关 键 词：左R-模 Riesz空间范畴 内射对象 可裂性 乘积性 

分 类 号：O154[理学—数学] O159[理学—基础数学]