摘要
本文研究了McCoy环上的循环模和有限生成模的McCoy性,得到一定条件下,McCoy环上的左循环模是McCoy模,并分别给出了一个McCoy环上的单模均为McCoy模,以及一个非McCoy环上的单模是McCoy模的例子.最后证明在一定条件下,环R上的有限生成自由模是McCoy模的充要条件是环R为McCoy环.
In this article,we study the McCoy modules of cyclic modules and nitely generated modules over a McCoy ring.We show that a left cyclic module over a McCoy ring is a McCoy module under some condition.We give examples to show that a simple module over a McCoy ring is McCoy and a simple module over a non-McCoy ring is McCoy respectively.We also show that the nitely generated free modules under some conditions over a ring R are McCoy if and only if the ring R is McCoy.
作者
李梅
宦明蕾
程智
LI Mei;HUAN Minglei;CHENG Zhi(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,China;The NO.1 Senior Middle School of Xiayi County,Shangqiu 476400,China)
出处
《纯粹数学与应用数学》
2024年第1期162-167,共6页
Pure and Applied Mathematics
基金
安徽省自然科学基金项目(2008085MA06)
安徽省高校自然科学重点基金(KJ2019A0488)。
