Geodesic
On $n$-submodules and $G.n$-submodules
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 245-262
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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 \hbox {$G.n$-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.
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 \hbox {$G.n$-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.
DOI : 10.21136/CMJ.2022.0094-22
Classification : 13C13, 16D10
Keywords: $n$-ideal; $n$-submodule; primary submodule 
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Karimzadeh, Somayeh; Moghaderi, Javad. On $n$-submodules and $G.n$-submodules. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 245-262. doi: 10.21136/CMJ.2022.0094-22

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