Ω-左R-模范畴中投射对象性质研究  

Research on Properties of the Projective Object in the Category ofΩ-Left R-Modules

作　　者：郭云涛 汤建钢 周鑫 GUO Yun-tao;TANG Jian-gang;ZHOU Xin(College of Mathematics and statistics,Yili Normal University,Yining 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

出　　处：《数学的实践与认识》2021年第14期206-217,共12页Mathematics in Practice and Theory

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

摘　　要：引入Ω-左R-模范畴中投射对象概念,研究Ω-左R-模范畴中投射对象的等价刻画,证明Ω-左R-模范畴中一簇对象的直和是投射对象当且仅当簇中每一个都是投射对象,一个Ω-左R-模是投射对象当且仅当它的每一个截集是投射左R-模.In this paper,we introduce the concept of projective object in the category ofΩ-left R-modules,equivalent descriptions of an projective object in the category ofΩ-left Rmodules is investigated,a product of a bunch ofΩ-left R-modules is an projective object if and only if every one is an projective object is proved,aΩ-left R-module is an projective object if and only if it’s every cut sets is proved to be an projective object.

关 键 词：Ω-左R-模范畴 Ω-集合范畴 投射对象 

分 类 号：O154.1[理学—数学]