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On modules and rings with the restricted minimum condition

Volume 140 / 2015

M. Tamer Koşan, Jan Žemlička Colloquium Mathematicum 140 (2015), 75-86 MSC: Primary 16D40; Secondary 16E50. DOI: 10.4064/cm140-1-6


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.


  • M. Tamer KoşanDepartment of Mathematics
    Gebze Technical University
    41400 Gebze/Kocaeli, Turkey
  • Jan ŽemličkaDepartment of Algebra
    Faculty of Mathematics and Physics
    Charles University in Prague
    Sokolovská 83
    186 75 Praha 8, Czech Republic

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