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 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/Soc(R) is noetherian and every singular module is semiartinian.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-6,
author = {M. Tamer Ko\c san and Jan \v Zemli\v cka},
title = {On modules and rings with the restricted minimum condition},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {75-86},
zbl = {1338.16008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-6}
}
M. Tamer Koşan; Jan Žemlička. On modules and rings with the restricted minimum condition. Colloquium Mathematicae, Tome 139 (2015) pp. 75-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-6/