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E*_essential submodule
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Publication Date
Tue Sep 01 2015
Journal Name
Journal Of Al-nahrain University-science
St-closed Submodule
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Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.

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Publication Date
Wed Sep 12 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
W-Closed Submodule and Related Concepts
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    Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.   

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Publication Date
Thu Apr 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Strongly Pseudo Nearly Semei-2-Absorbing Submodule(I)
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Let  be a module over a commutative ring  with identity. In this paper we intoduce the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, where a  proper submodule  of an -module  is said to be Strongly Pseudo Nearly Semi-2-Absorbing submodule of   if whenever , for implies that either  or , this concept is a generalization of 2_Absorbing submodule, semi 2-Absorbing submodule, and strong form of (Nearly–2–Absorbing, Pseudo_2_Absorbing, and Nearly Semi–2–Absorbing) submodules. Several properties characterizations, and examples concerning this new notion are given. We study the relation between Strongly Pseudo Nearly Semei-2-Absorbing submodule and (2_Absorbing, Nearly_2_Absorbing, Pseudo_2_Absorbing, and Nearly S

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Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
SOME RESULTS ON T_PURE SUBMODULES RELATED TO SUBMODULE
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Abstract<p>The aim of this work is studying many concepts of a pure submodule related to sub-module L and introducing the two concepts, T_pure submodule related to submodule and the crossing property of T_pure related to submodule. Another characterizations and study some properties of this concept.</p>
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Publication Date
Sun Dec 06 2015
Journal Name
Baghdad Science Journal
Some Results on Pure Submodules Relative to Submodule
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Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Large-Small submodule and Large-Hollow module
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Abstract<p>The goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤<sub>e</sub> M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.</p>
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Publication Date
Tue Nov 30 2021
Journal Name
Journal Of The Indonesian Mathematical Society
e*-Hollow-Lifting and Cofinitely e*-Lifting Modules
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Publication Date
Sat Apr 30 2022
Journal Name
European Journal Of Pure And Applied Mathematics
e*-Essential small submodules and e*-hollow module
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Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
E-small prime sub-modules and e-small prime modules
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Publication Date
Thu Nov 02 2023
Journal Name
Missouri Journal Of Mathematical Sciences
e*_lifting midule
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