On modules and rings with the restricted minimum condition
Tom 140 / 2015
Colloquium Mathematicum 140 (2015), 75-86
MSC: Primary 16D40; Secondary 16E50.
DOI: 10.4064/cm140-1-6
Streszczenie
A module $M$ satisfies the restricted minimum condition if $M/N$ is artinian for every essential submodule $N$ of $M$. A ring $R$ is called a right RM-ring whenever $R_R$ satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring $R$ is proved to be an RM-ring if and only if $R/\operatorname {Soc}(R)$ is noetherian and every singular module is semiartinian.
