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jih-117
á´ª-Prime Submodules
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      Let R be a commutative ring with identity and M be 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 -prime if for each r  R and x  M, if rx  P, then either x  P + (P) or r M  P + (P) . Some of the properties of this concept will be investigated. Some characterizations of -prime submodules will be given, and we show that under some assumptions prime submodules and -prime submodules are coincide. 

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Publication Date
Mon Mar 01 2021
Journal Name
Journal Of Physics: Conference Series
On Quasi-Small Prime Modules
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Abstract<p>Let R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.</p>
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Publication Date
Mon May 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Dual Notions of Prime Modules
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       Let R be a commutative ring with unity .M an R-Module. M is called coprime module     (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M   In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.

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Publication Date
Wed Jan 01 2020
Journal Name
Italian Journal Of Pure And Applied Mathematics
Duality of St-closed submodules and semi-extending modules
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The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

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Publication Date
Mon Sep 16 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Pseudo Primary-2-Absorbing Submodules and Some Related Concepts
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      Let  be a commutative ring with identity. The aim of this paper is introduce the notion of a pseudo primary-2-absorbing submodule as generalization of 2-absorbing submodule and a pseudo-2-absorbing submodules. A proper submodule  of an -module  is called pseudo primary-2-absorbing if whenever , for , , implies that either                  or  or . Many basic properties, examples and characterizations of these concepts are given. Furthermore, characterizations of pseudo primary-2-absorbing submodules in some classes of modules are introduced. Moreover, the behavior of a pseudo primary-2-absorbing submodul

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Publication Date
Tue Feb 28 2023
Journal Name
Iraqi Journal Of Science
Orthogonal Generalized Higher k-Derivation on Semi Prime Г-Rings
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The definition of orthogonal generalized higher k-derivation is examined in this paper and we introduced some of its related results.

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Publication Date
Sun Mar 01 2009
Journal Name
Baghdad Science Journal
Some Results On Lie Ideals With (&#963;,&#964;)-derivationIn Prime Rings
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In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

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Publication Date
Fri Mar 01 2024
Journal Name
Baghdad Science Journal
On Existence of Prime K-Tuples Conjecture for Positive Proportion of Admissible K-Tuples
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Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

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Publication Date
Sun Jan 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
T-ABSO T-Abso and T-Abso Quasi Primary Fuzzy Submodules
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     Let Ḿ be a unitary R-module and R is a commutative ring with identity. Our aim in this paper  to study the concepts T-ABSO fuzzy ideals, T-ABSO fuzzy submodules and T-ABSO quasi primary fuzzy submodules, also we discuss these concepts in the class of multiplication fuzzy modules and relationships between these concepts. Many new basic properties and characterizations on these concepts are given.

 

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Publication Date
Thu Jan 20 2022
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Strongly Maximal Submodules with A Study of Their Influence on Types of Modules
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      Let S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Lie and Jordan Structure in Prime Γ- rings with Γ-centralizing Derivations
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Let M be a prime Γ-ring satisfying abc  abc for all a,b,cM and
,  with center Z, and U be a Lie (Jordan) ideal. A mapping d :M M
is called Γ- centralizing if u d u Z  [ , ( )] for all uU and  .In this paper
, we studied Lie and Jordan ideal in a prime Γ - ring M together with Γ -
centralizing derivations on U.

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