Riesz模范畴中自由函子的伴随性  

Adjoint Property of Free Functor in the Category of Riesz Module

作　　者：王金萌 汤建钢 Wang Jinmeng;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）》2024年第2期1-5,共5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空间的相关研究,给出了Riesz模范畴的概念,研究了Riesz模范畴中自由函子的伴随性及可裂性,证明了自由函子与遗忘函子是一对伴随函子,以及自由Riesz模F的一个满同态ϕ:M→F是可裂的.Based on the study of Riesz spaces on left R-modules,the concept of the category of Riesz modules is given,the adjoint and cleavability properties of free functor in the category of Riesz modules are studied,and it is proved that free functors and forgetting functors are a pair of adjoint functors,and a full homomorphismϕ:M→F of free Riesz modules F is cleavable.

关 键 词：Riesz模范畴 自由函子 伴随性 

分 类 号：O154[理学—数学] O159[理学—基础数学]