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ijs-6941
Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings

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
Mon Oct 28 2019
Journal Name
Iraqi Journal Of Science
Generalized Strong Commutativity Preserving Centralizers of Semiprime Γ- Rings

     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
Fri Jun 30 2023
Journal Name
Iraqi Journal Of Science
On Г-n- (Anti ) Generalized Strong Commutativity Preserving Maps for Semiprime Γ-Rings

      In this study, we prove that let N be a fixed positive integer and R be a semiprime -ring with extended centroid . Suppose that additive maps  such that  is onto,  satisfy one of the following conditions  belong to Г-N- generalized strong commutativity preserving for short; (Γ-N-GSCP) on R   belong to Г-N-anti-generalized strong commutativity preserving for short; (Γ-N-AGSCP)  Then there exists an element  and  additive maps  such that  is of the form  and   when condition (i) is satisfied, and     when condition (ii) is satisfied   

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Publication Date
Fri Jan 26 2024
Journal Name
Iraqi Journal Of Science
On Reverse – Centralizers Of Semiprime Rings

In this paper we study necessary and sufficient conditions for a reverse- centralizer of a semiprime ring R to be orthogonal. We also prove that a reverse- centralizer T of a semiprime ring R having a commuting generalized inverse is orthogonal

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Publication Date
Sun Dec 05 2010
Journal Name
Baghdad Science Journal
Jordan ?-Centralizers of Prime and Semiprime Rings

The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R. Then T is a left (right) ?-centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where ? be surjective endomorphism of R . It is also proved that if T(x?y)=T(x)??(y)=?(x)?T(y) for all x, y ? R and ?-centralizers of R coincide under same condition and ?(Z(R)) = Z(R) .

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Publication Date
Sat Jul 31 2021
Journal Name
Iraqi Journal Of Science
On Centralizers of 2-torsion Free Semiprime Gamma Rings

In this paper, we prove that; Let M be a 2-torsion free semiprime  which satisfies the condition  for all  and α, β . Consider that  as an additive mapping such that  holds for all  and α , then T is a left and right centralizer.

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Publication Date
Mon Jan 10 2022
Journal Name
Iraqi Journal Of Science
Centralizers on Prime and Semiprime Γ-rings

In this paper, we will generalized some results related to centralizer concept on
prime and semiprime Γ-rings of characteristic different from 2 .These results
relating to some results concerning left centralizer on Γ-rings.

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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

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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Scopus (5)
Crossref (1)
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Publication Date
Wed Aug 31 2022
Journal Name
Iraqi Journal Of Science
Generalized Commuting Mapping in Prime and Semiprime Rings

     Let R be an associative ring. The essential purpose of the present paper is to introduce the concept of generalized commuting mapping of R. Let U be a non-empty subset of R, a mapping   : R  R is called a generalized commuting mapping on U if there exist a mapping :R R such that =0, holds for all U. Some results concerning the new concept are presented.

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Publication Date
Sun Apr 29 2018
Journal Name
Iraqi Journal Of Science
Orthogonal Generalized Symmetric Higher bi-Derivations on Semiprime Г-Rings .

In this paper a Г-ring M is presented. We will study the concept of orthogonal generalized symmetric higher bi-derivations on Г-ring. We prove that if M is a 2-torsion free semiprime    Г-ring ,  and  are orthogonal generalized symmetric higher bi-derivations  associated with symmetric higher bi-derivations   respectively for all n ϵN.

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Publication Date
Sun Jul 02 2023
Journal Name
Iraqi Journal Of Science
Nilpotency of Centralizers in Prime Rings

Nilpotency of Centralizers in Prime Rings

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