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ijs-1035
Almost Pure Ideals (Submodules) and Almost Regular Rings (Modules)
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     Let R1be a commutative2ring with identity and M be a unitary R-module. In this6work we7present almost pure8ideal (submodule) concept as a9generalization of pure10ideal (submodule).  lso, we1generalize some9properties of8almost pure ideal (submodule). The 7study is almost regular6ring (R-module).

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Publication Date
Wed May 25 2022
Journal Name
Iraqi Journal Of Science
F-J-semi Regular Modules
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      Let  be a ring with identity and let  be a left R-module. If is  a proper submodule of  and  ,  is called --semi regular element in  , If there exists a decoposition  such that  is projective submodule of  and  . The aim of this paper is to introduce properties of F-J-semi regular module. In particular, its characterizations are given. Furthermore, we introduce the concepts of Jacobson hollow semi regular module and --semiregular module. Finally, many results of Jacobson hollow semi regular module and --semiregular module are presented.

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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
J-semi regular modules
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Abstract<p>Let <italic>R</italic> be a ring with identity and let <italic>M</italic> be a left R-module. <italic>M</italic> is called J-semiregular module if every cyclic submodule of <italic>M</italic> is J-lying over a projective summand of <italic>M</italic>, The aim of this paper is to introduce properties of J-semiregular module Especially, we give characterizations of J-semiregular module. On the other hand, the notion of J-semi hollow modules is studied as a generalization of semi hollow modules, finally <italic>F</italic>-J-semiregular modules is studied as a generalization of <italic>F</italic>-semiregular modules.</p> ... Show More
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Publication Date
Sun Dec 01 2013
Journal Name
Baghdad Science Journal
Notes on Approximately Pure Submodules
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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 approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

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Publication Date
Wed Aug 31 2022
Journal Name
Iraqi Journal Of Science
2-prime submodules of modules
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      Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

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Publication Date
Sat Jan 01 2022
Journal Name
Iraqi Journal Of Science,
F-J-semi Regular Modules Department
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Publication Date
Fri Oct 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Pure Maximal Submodules and Related Concepts
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      In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule  of an R-module  is called Pr- maximal if  ,for any submodule  of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule  

 of an R-module  is named near (N-maximal) whensoever  is pure submodule of  such that  then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of  is Pr-maximal. A ring  is named Pr-ring if whole proper ideal of  is a Pr-maximal ideal, we offer the concept pure local (Pr-loc

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Publication Date
Thu May 28 2020
Journal Name
Iraqi Journal Of Science
Semiprime RΓ-Submodules of Multiplication RΓ-Modules
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Let R be a Γ-ring and G be an RΓ-module. A proper RΓ-submodule S of G is said to be semiprime RΓ-submodule if for any ideal I of a Γ-ring R and for any RΓ-submodule A of G such that or which implies that . The purpose of this paper is to introduce interesting results of semiprime RΓ-submodule of RΓ-module which represents a generalization of semiprime submodules.

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Publication Date
Fri Dec 30 2022
Journal Name
Iraqi Journal Of Science
Purely Small Submodules and Purely Hollow Modules
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         The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.

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Publication Date
Wed Jun 26 2019
Journal Name
Iraqi Journal Of Science
H-essential Submodules and Homessential Modules
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The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules. Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given. Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.

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Publication Date
Sun Oct 20 2024
Journal Name
Baghdad Science Journal
Modules Whose St-Closed Submodules are Fully Invariant
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The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl

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