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Near – Rings with Generalized Right n-Derivations
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We define a new concept, called " generalized right  -derivation", in near-ring and obtain new essential results in this field. Moreover we improve this paper with examples that show that the assumptions used are necessary.

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Orthogonal Derivations and Orthogonal Generalized Derivations on - Modules
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Let M be ,-ring and X be ,M-module, Bresar and Vukman studied orthogonal
derivations on semiprime rings. Ashraf and Jamal defined the orthogonal derivations
on -rings M. This research defines and studies the concepts of orthogonal
derivation and orthogonal generalized derivations on ,M -Module X and introduces
the relation between the products of generalized derivations and orthogonality on
,M -module.

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Publication Date
Wed Jul 17 2019
Journal Name
Iraqi Journal Of Science
On Commutativity of Prime and Semiprime - Rings with Reverse Derivations
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Let M be a weak Nobusawa -ring and γ be a non-zero element of Γ. In this paper, we introduce concept of k-reverse derivation, Jordan k-reverse derivation, generalized k-reverse derivation, and Jordan generalized k-reverse derivation of Γ-ring, and γ-homomorphism, anti-γ-homomorphism of M. Also, we give some commutattivity conditions on γ-prime Γ-ring and γ-semiprime Γ-ring .

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Publication Date
Sun Jun 02 2019
Journal Name
Baghdad Science Journal
On Skew Left n-Derivations with Lie Ideal Structure
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In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

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Publication Date
Mon Oct 28 2019
Journal Name
Iraqi Journal Of Science
Generalized Strong Commutativity Preserving Centralizers of Semiprime Γ- Rings
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     In this paper, we introduce the concept of generalized strong commutativity (Cocommutativity) preserving right centralizers on a subset of a Γ-ring. And we generalize some results of a classical ring to a gamma ring.

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Publication Date
Wed Jan 12 2022
Journal Name
Iraqi Journal Of Science
Jordan Permuting 3-Derivations of Prime Rings
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The main purpose of this work is to generalize Daif's result by introduceing the concept of Jordan (α β permuting 3-derivation on Lie ideal and generalize these result by introducing the concept of generalized Jordan (α β permuting 3-derivation 

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Publication Date
Tue Sep 29 2020
Journal Name
Iraqi Journal Of Science
A Jordan Higher Reverse Left (resp. right) Centralizer on Prime -Rings
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In this paper,  we introduce the concepts of  higher reverse left (resp.right)   centralizer, Jordan higher reverse left (resp. right) centralizer, and Jordan triple higher reverse left (resp. right) centralizer of  G-rings. We prove that every Jordan higher reverse left (resp. right) centralizer of a 2-torsion free prime G-ring M is a higher reverse left (resp. right) centralizer of  M.

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Publication Date
Thu Apr 28 2022
Journal Name
Iraqi Journal Of Science
Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings
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Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of R. An additive mappings are called right centralizer if ( ) ( ) and ( ) ( ) holds for all . In the present paper, we introduce the concepts of generalized strong commutativity centralizers preserving and generalized strong cocommutativity preserving centralizers and we prove that R contains a nonzero central ideal if any one of the following conditions holds: (i) ( ) ( ), (ii) [ ( ) ( )] , (iii) [ ( ) ( )] [ ], (iv) ( ) ( ) , (v) ( ) ( ) , (vi) [ ( ) ( )] , (vii) ( ) ( ) ( ), (viii) ( ) ( ) for all .

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Publication Date
Thu Dec 29 2016
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
(,)- Strongly Derivations Pairs on Rings
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        Let R be an associative ring. In this paper we present the definition of (s,t)- Strongly derivation pair and Jordan (s,t)- strongly derivation pair on a ring R, and study the relation between them. Also, we study prime rings, semiprime rings, and rings that have commutator left nonzero divisior with (s,t)- strongly derivation pair, to obtain a (s,t)- derivation. Where s,t: R®R are two mappings of R.

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Publication Date
Thu Nov 29 2018
Journal Name
Iraqi Journal Of Science
On Skew Left ∗-n-Derivations of ∗-Ring
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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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