Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 245-262, 2023
On $n$-submodules and $G.n$-submodules
Somayeh Karimzadeh, Javad Moghaderi
Received March 5, 2022. Published online December 12, 2022.
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.
Affiliations: Somayeh Karimzadeh (corresponding author), Vali-e-Asr University of Rafsanjan, Imam Khomeini Square, P. O. Box 7718897111, Rafsanjan, Iran, e-mail: karimzadeh@vru.ac.ir; Javad Moghaderi, University of Hormozgan, Minab Road, 7916193145, Bandar Abbas, Iran, e-mail: j.moghaderi@hormozgan.ac.ir
