Ω-左R-模范畴中内射对象的等价刻画  

Equivalent Characterizations of the Injective Objects in the Category of Ω-Left R-Modules

作　　者：黄美丽 汤建钢 周鑫 HUANG Mei-li;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》2020年第16期250-261,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11161050,31424020);2019年度自治区高校科研计划自然科学重点项目(XJEDU20191024)

摘　　要：引入内射Ω-左R-模的概念,研究内射Ω-左R-模的等价刻画,证明一簇Ω-左R-模的乘积是内射Ω-左R-模当且仅当每一个是内射Ω-左R-模,一个Ω-左R-模是内射Ω-左R-模当且仅当它的每一个截集是内射左R-模.In this paper,we introduce the concept of injective object in the category ofΩ-left R-modules,equivalent descriptions of an injective object in the category of Ω-left Rmodules is investigated,a product of a bunch of Ω-left R-modules is an injective object if and only if every one is an injective object is proved,a Ω-left R-module is an injective object if and only if it’s every cut sets is proved to be an injective object.

关 键 词：Ω-左R-模范畴 Ω-集合范畴 内射对象 

分 类 号：O154.1[理学—数学]