On modules and rings
 with the restricted minimum condition

M. Tamer Koşan; Jan Žemlička

doi:10.4064/cm140-1-6

Geodesic

Parcourir par

On modules and rings with the restricted minimum condition

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

Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 75-86.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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

Affiliations des auteurs :

M. Tamer Koşan ¹ ; Jan Žemlička ²

@article{10_4064_cm140_1_6,
     author = {M. Tamer Ko\c{s}an and Jan \v{Z}emli\v{c}ka},
     title = {On modules and rings
 with the restricted minimum condition},
     journal = {Colloquium Mathematicum},
     pages = {75--86},
     publisher = {mathdoc},
     volume = {140},
     number = {1},
     year = {2015},
     doi = {10.4064/cm140-1-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm140-1-6/}
}

TY  - JOUR
AU  - M. Tamer Koşan
AU  - Jan Žemlička
TI  - On modules and rings
 with the restricted minimum condition
JO  - Colloquium Mathematicum
PY  - 2015
SP  - 75
EP  - 86
VL  - 140
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm140-1-6/
DO  - 10.4064/cm140-1-6
LA  - en
ID  - 10_4064_cm140_1_6
ER  -

%0 Journal Article
%A M. Tamer Koşan
%A Jan Žemlička
%T On modules and rings
 with the restricted minimum condition
%J Colloquium Mathematicum
%D 2015
%P 75-86
%V 140
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm140-1-6/
%R 10.4064/cm140-1-6
%G en
%F 10_4064_cm140_1_6

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. http://geodesic.mathdoc.fr/articles/10.4064/cm140-1-6/

Cité par Sources :