On modules and rings with the restricted minimum condition

M. Tamer Koşan, and Jan Žemlička. "On modules and rings with the restricted minimum condition." Colloquium Mathematicae 140.1 (2015): 75-86. <http://eudml.org/doc/284332>.

@article{M2015,
abstract = {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/Soc(R) is noetherian and every singular module is semiartinian.},
author = {M. Tamer Koşan, Jan Žemlička},
journal = {Colloquium Mathematicae},
keywords = {restricted minimum condition; singular modules; semiartinian rings; semilocal rings; max rings; perfect rings},
language = {eng},
number = {1},
pages = {75-86},
title = {On modules and rings with the restricted minimum condition},
url = {http://eudml.org/doc/284332},
volume = {140},
year = {2015},
}

TY - JOUR
AU - M. Tamer Koşan
AU - Jan Žemlička
TI - On modules and rings with the restricted minimum condition
JO - Colloquium Mathematicae
PY - 2015
VL - 140
IS - 1
SP - 75
EP - 86
AB - 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/Soc(R) is noetherian and every singular module is semiartinian.
LA - eng
KW - restricted minimum condition; singular modules; semiartinian rings; semilocal rings; max rings; perfect rings
UR - http://eudml.org/doc/284332
ER -