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On δ-small M-Projective Modules
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In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.

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Publication Date
Sun May 26 2019
Journal Name
Iraqi Journal Of Science
On H-µ-supplemented modules
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Weosay thatotheosubmodules A, B ofoan R-module Moare µ-equivalent , AµB ifoand onlyoif <<µand <<µ. Weoshow thatoµ relationois anoequivalent relationoand hasegood behaviorywith respectyto additionmof submodules, homorphismsr, andydirectusums, weaapplyothese resultsotoointroduced theoclassoof H-µ-supplementedomodules. Weosay thatoa module Mmis H-µ-supplementedomodule ifofor everyosubmodule A of M, thereois a directosummand D ofoM suchothat AµD. Variousoproperties ofothese modulesoarepgiven.

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Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(7)
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  The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs.         All of these arcs are incomplete.         The number of distinct (12,3)-arcs are six, two of them are complete.         There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete.         There exists one complete (15,3)-arc.
 

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Publication Date
Sun Apr 26 2020
Journal Name
Iraqi Journal Of Science
On Hollow – J–Lifting Modules
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In this paper, we introduce and study the concepts of hollow – J–lifting modules and FI – hollow – J–lifting modules as a proper generalization of both hollow–lifting and J–lifting modules . We call an R–module M as hollow – J – lifting if for every submodule N of M with is hollow, there exists a submodule K of M such that M = K Ḱ and K N in M . Several characterizations and properties of hollow –J–lifting modules are obtained . Modules related to hollow – J–lifting modules are  given .

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Publication Date
Sat Apr 30 2022
Journal Name
Iraqi Journal Of Science
On Large-Lifting and Large-Supplemented Modules
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      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

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Publication Date
Sun Feb 27 2022
Journal Name
Iraqi Journal Of Science
On Strong Dual Rickart Modules
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    Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to define strong dual Rickart module. Let M and N be R- modules , M is called N- strong dual Rickart module (or relatively sd-Rickart to N)which is  denoted by M it is N-sd- Rickart if for every submodule A of M and every homomorphism fHom (M , N) , f (A) is a direct summand of N. We prove that for an R- module M , if R is M-sd- Rickart , then every cyclic submodule of M is a direct summand . In particular, if M<

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Publication Date
Sun Apr 30 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9)
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  In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.

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Publication Date
Wed Oct 28 2020
Journal Name
Iraqi Journal Of Science
On y-closed Rickart Modules
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     In a previous work, Ali and Ghawi studied closed Rickart modules. The main purpose of this paper is to define and study the properties of y-closed Rickart modules .We prove that, Let  and   be two -modules such that  is singular. Then  is -y-closed Rickart module if and only if   Also, we study the direct sum  of  y-closed Rickart modules.

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Publication Date
Sun Dec 04 2011
Journal Name
Baghdad Science Journal
Approximate Regular Modules
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There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

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Publication Date
Fri Jun 30 2023
Journal Name
Iraqi Journal Of Science
On (k,m)-n-Paranormal Operators
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     The new type of paranormal operators that have been defined in this study on the Hilbert space, is  paranormal operators. In this paper we introduce and discuss some properties of this concept such as: the sum and product of two paranormal, the power of paranormal. Further, the relationships between the paranormal operators and other kinds of paranormal operators have been studied.

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Publication Date
Thu Mar 30 2023
Journal Name
Iraqi Journal Of Science
On (m,n) (U,R) – Centralizers
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Let m ≥ 1,n ≥ 1 be fixed integers and let R be a prime ring with char (R) ≠2 and
(m+n). Let T be a (m,n)(U,R)-Centralizer where U is a Jordan ideal of R and T(R)
⊆ Z(R) where Z(R) is the center of R ,then T is (U,R)- Centralizer.

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