On $n$-submodules and $G.n$-submodules

Karimzadeh, Somayeh, and Moghaderi, Javad. "On $n$-submodules and $G.n$-submodules." Czechoslovak Mathematical Journal 73.1 (2023): 245-262. <http://eudml.org/doc/299510>.

@article{Karimzadeh2023,
abstract = {We investigate some properties of $n$-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an $n$-submodule. Also, we show that if $M$ is a finitely generated $R$-module and $ \sqrt\{\{\{\rm Ann\} \}_R(M)\}$ is a prime ideal of $R$, then $M$ has $n$-submodule. Moreover, we define the notion of $G.n$-submodule, which is a generalization of the notion of $n$-submodule. We find some characterizations of $G.n$-submodules and we examine the way the aforementioned notions are related to each other.},
author = {Karimzadeh, Somayeh, Moghaderi, Javad},
journal = {Czechoslovak Mathematical Journal},
keywords = {$n$-ideal; $n$-submodule; primary submodule},
language = {eng},
number = {1},
pages = {245-262},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $n$-submodules and $G.n$-submodules},
url = {http://eudml.org/doc/299510},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Karimzadeh, Somayeh
AU - Moghaderi, Javad
TI - On $n$-submodules and $G.n$-submodules
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 1
SP - 245
EP - 262
AB - We investigate some properties of $n$-submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an $n$-submodule. Also, we show that if $M$ is a finitely generated $R$-module and $ \sqrt{{{\rm Ann} }_R(M)}$ is a prime ideal of $R$, then $M$ has $n$-submodule. Moreover, we define the notion of $G.n$-submodule, which is a generalization of the notion of $n$-submodule. We find some characterizations of $G.n$-submodules and we examine the way the aforementioned notions are related to each other.
LA - eng
KW - $n$-ideal; $n$-submodule; primary submodule
UR - http://eudml.org/doc/299510
ER -