Geodesic
On modules and rings with the restricted minimum condition
M. Tamer Koşan1 ; Jan Žemlička2
1 Department of Mathematics Gebze Technical University 41400 Gebze/Kocaeli, Turkey
2 Department of Algebra Faculty of Mathematics and Physics Charles University in Prague Sokolovská 83 186 75 Praha 8, Czech Republic
Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 75-86 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm140-1-6
Keywords: module satisfies restricted minimum condition artinian every essential submodule ring called right rm ring whenever satisfies restricted minimum condition right module several structural necessary conditions particular classes rm rings furthermore commutative ring proved rm ring only operatorname soc noetherian every singular module semiartinian

M. Tamer Koşan 1 ; Jan Žemlička 2

1 Department of Mathematics Gebze Technical University 41400 Gebze/Kocaeli, Turkey
2 Department of Algebra Faculty of Mathematics and Physics Charles University in Prague Sokolovská 83 186 75 Praha 8, Czech Republic 
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M. Tamer Koşan; Jan Žemlička. On modules and rings
 with the restricted minimum condition. Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 75-86. doi: 10.4064/cm140-1-6

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