商模的McCoy性  

The McCoy property of quotient module

作　　者：宦明蕾 程智 HUAN Mingei;CHENG Zhi(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《纯粹数学与应用数学》2024年第4期738-745,共8页Pure and Applied Mathematics

基　　金：安徽省高校自然科学重点基金(KJ2019A0488).

摘　　要：首先引入环R上模M相关于其子模M′的商McCoy模的概念,利用箭图工具绘出例子说明在非交换环上存在商McCoy模,并且构造实例说明交换环上的商模未必都是商McCoy模.然后证明了若M是关于其子模M′的商McCoy模,则商模M/M′是McCoy模.最后研究了一类矩阵环上的商McCoy模及多项式环上的商McCoy模.Firstly,the concept of quotient McCoy module M over the ring R correlation with its submodule M′is introduced.The quvier tool is used to draw an example to show the existence of quotient McCoy module on a non-commutative ring.And example is given to illustrate that quotient modules on commutative rings may not be quotient McCoy modules.Then proved that the quotient module M/M′is McCoy if M is a quotient McCoy module correlation with its submodule M′.Finally,the quotient McCoy modules on a kind of matrix ring and polynomial ring are researched.

关 键 词：McCoy模 商McCoy模 子模 

分 类 号：O153.3[理学—数学]