S-prime and S-weakly prime submodules
EA Ugurlu - arXiv preprint arXiv:2005.08733, 2020 - arxiv.org
In this study, all rings are commutative with non-zero identity and all modules are considered
to be unital. Let $ M $ be a left $ R $-module. A proper submodule $ N $ of $ M $ is called an …
to be unital. Let $ M $ be a left $ R $-module. A proper submodule $ N $ of $ M $ is called an …
On weakly S-prime submodules
HA Khashan, EY Celikel - arXiv preprint arXiv:2110.14639, 2021 - arxiv.org
Let $ R $ be a commutative ring with a non-zero identity, $ S $ be a multiplicatively closed
subset of $ R $ and $ M $ be a unital $ R $-module. In this paper, we define a submodule …
subset of $ R $ and $ M $ be a unital $ R $-module. In this paper, we define a submodule …
---primary submodule
S Najafi, S Ghalandarzadeh, ARN Esfahani… - arXiv preprint arXiv …, 2023 - arxiv.org
In this paper, we introduce and investigate some properties of $\phi $-$\delta $-$ S $-
primary submodules, which is a generalization of the $\phi $-$\delta $-primary submodules …
primary submodules, which is a generalization of the $\phi $-$\delta $-primary submodules …
Weakly classical prime submodules
H Mostafanasab, U Tekir, KH Oral - arXiv preprint arXiv:1505.06730, 2015 - arxiv.org
In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …
-Weakly second submodules
IE Wijayanti, DA Yuwaningsih… - Asian-European Journal of …, 2019 - World Scientific
We introduce the dual notions of S (N)-weakly prime submodules, that is, S (0)-weakly
second submodules in a commutative ring with identity. We investigate the properties of S …
second submodules in a commutative ring with identity. We investigate the properties of S …
S-small and S-essential submodules
S Rajaee - arXiv preprint arXiv:2109.00519, 2021 - arxiv.org
This paper is concerned with S-co-m modules which are a generalization of co-m modules.
In section 2, we introduce the S-small and S-essential submodules of a unitary $ R $-module …
In section 2, we introduce the S-small and S-essential submodules of a unitary $ R $-module …
[引用][C] Generalizations of -semiprime submodules
P Ghiasvand, F Farzalipour - Asian-European Journal of …, 2023 - World Scientific
Let R be a commutative ring with non-zero identity, S⊆ R a multiplicatively closed subset of
R and M a unital R-module. In this paper, we introduce the concepts of S-almost semiprime …
R and M a unital R-module. In this paper, we introduce the concepts of S-almost semiprime …
On Almost $ S $-prime submodules
F Farzalipour, R Ghaseminejad… - Journal of Algebra and …, 2023 - jart.guilan.ac.ir
Let $ R $ be a commutative ring with non-zero identity, $ S\subseteq R $ be a
multiplicatively closed subset of $ R $ and let $ M $ be an $ R $-module. A submodule $ N …
multiplicatively closed subset of $ R $ and let $ M $ be an $ R $-module. A submodule $ N …
[引用][C] On weakly prime submodules
F Farzalipour - Tamkang Journal of Mathematics, 2007 - airitilibrary.com
Let R be a commutative ring with non-zero identity. We define a proper submodule N of an R-
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …
On weakly prime submodules
SE Atani, F Farzalipour - Tamkang Journal of Mathematics, 2007 - journals.math.tku.edu.tw
Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $
of an $ R $-module $ M $ to be weakly prime if $0\not= rm\in N $($ r\in R, m\in M $) implies …
of an $ R $-module $ M $ to be weakly prime if $0\not= rm\in N $($ r\in R, m\in M $) implies …