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bsj-2839
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
Tue Nov 13 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
WE-Prime Submodules and WE-Semi-Prime Submodules
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"In this article, "we introduce the concept of a WE-Prime submodule", as a stronger form of a weakly prime submodule". "And as a "generalization of WE-Prime submodule", we introduce the concept of WE-Semi-Prime submodule, which is also a stronger form of a weakly semi-prime submodule". "Various basic properties of these two concepts are discussed. Furthermore, the relationships between "WE-Prime submodules and weakly prime submodules" and studied". "On the other hand the relation between "WE-Prime submodules and WE-Semi-Prime submodules" are consider". "Also" the relation of "WE-Sime-Prime submodules and weakly semi-prime submodules" are explained. Behind that, some characterizations of these concepts are investigated".

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Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Fuzzy Semimaximal Submodules
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     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

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Publication Date
Sat Mar 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
End á´ª -Prime Submodules
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      Let R be a commutative ring with identity and M  an unitary R-module. Let (M)  be the set of all submodules of M, and : (M)  (M)  {} be a function. We say that a proper submodule P of M is end--prime if for each   EndR(M) and x  M, if (x)  P, then either x  P + (P) or (M)  P + (P). Some of the properties of this concept will be investigated. Some characterizations of end--prime submodules will be given, and we show that under some assumtions prime submodules and end--prime submodules are coincide.

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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
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Injectivity and chain conditions on y-closed submodules
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Let R be a commutative ring with identity and let M be a unital left Rmodule.
Goodearl introduced the following concept :A submodule A of an R –
module M is an y – closed submodule of M if is nonsingular.In this paper we
introduced an y – closed injective modules andchain condition on y – closed
submodules.

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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
Fri Dec 01 2017
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
COLOR VARIATION OF STREPTOPELIA DECAOCTO (AVIS, COLUMBIDAE) WITH SOME NOTES ON ENDOPARASITES
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The present paper includes a study of color variation in Iraqi Collared dove Streptopelia decaocto. Three different populations have been recognized: the southern population which belongs to the Indian race, the northern population to the Eurasian race; the dark and light color variation occurs in the Baghdad population because of hybridisation between the two races, found infected with two cestodes,  Raillietina echinobothrida found  in most of our specimens, while the dark face found beside R. echinobothrida infected with Idiogenes sp. getting it probably from vertebrate sources. We believe that most of the Baghdad population was intermediate between north and south races.

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Publication Date
Sun Apr 26 2020
Journal Name
Iraqi Journal Of Science
R-annihilator-Coessential and R-annihilator-Coclosed Submodules
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Let be a unitary left R-module on associative ring with identity. A submodule of is called -annihilator small if , where is a submodule of , implies that ann( )=0, where ann( ) indicates annihilator of in . In this paper, we introduce the concepts of -annihilator-coessential and - annihilator - coclosed submodules. We give many properties related with these types of submodules.

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Publication Date
Tue Nov 13 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
WN-2-Absorbing Submodules And WNS-2-Absorbing Submodules
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In''this"article, we"study",the"concept""of WN"-"2"-''Absorbing'''submodules and WNS''-''2''-''Absorbing"submodules as generalization of "weakly 2-absorbing and weakly semi 2-absorbing submodules respectively. We investigate some of basic properties, examples and characterizations of them. Also, prove, the class of WN-2-Absorbing "submodules is contained in the class of WNS-2-Absorbing "submodules. Moreover, many interesting results about these concepts, were proven.

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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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