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Publication Date

Mon Jan 10 2022

Journal Name

Iraqi Journal Of Science

Volume

58

Issue Number

2B

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Centralizers on Prime and Semiprime Γ-rings

Semiprime Γ-ring

Centralizers

Sameer

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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

Sun Dec 05 2010

Journal Name

Baghdad Science Journal

Jordan ?-Centralizers of Prime and Semiprime Rings

"prime ring

semiprime ring

left (right) centralizer

centralizer

Jordan centralizer

left (right) ? -centralizer

?-centralizer

Jordan ?-centralizer."

Abdulrahman H.

Mushreq I.

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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

Fri May 01 2020

Journal Name

Journal Of Physics: Conference Series

Semi-group Ideals on prime and semiprime Γ-Near - Rings with Γ- (λ,δ) – derivations

H. A.

A. H.

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AbstractLet h is Γ−(λ,δ) – derivation on prime Γ−near-ring G and K be a nonzero semi-group ideal of G and δ(K) = K, then the purpose of this paper is to prove the following :- (a) If λ is onto on G, λ(K) = K, λ(0) = 0 and h acts like Γ−hom. or acts like anti–Γ−hom. on K, then h(K) = {0}.(b) If h + h is an additive on K, then (G, +) is abelian.

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(1)

Publication Date

Fri Jan 26 2024

Journal Name

Iraqi Journal Of Science

On Reverse – Centralizers Of Semiprime Rings

Semiprime ring

left (right) reverse-centralizer

reverse-centralizer

orthogonal map

generalized inverse.

Ali

Fatin

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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

Sat Jul 31 2021

Journal Name

Iraqi Journal Of Science

On Centralizers of 2-torsion Free Semiprime Gamma Rings

Î“-ring

Prime Î“-ring

Semiprime Î“-ring

left centralizer

right centralizer

Jordan centralizer

Abdulkareem T.

Abulrahman H.

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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

Sun Jul 02 2023

Journal Name

Iraqi Journal Of Science

Nilpotency of Centralizers in Prime Rings

semiprime ring

prime ring

derivation

left (right) centralizer

centralizer

Jordan centralizer

nilpotent centralizer

Abdulrahman

Faten

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Nilpotency of Centralizers in Prime Rings

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Publication Date

Wed Nov 30 2022

Journal Name

Iraqi Journal Of Science

Jordan generalized Γ- (σ,τ) -Derivation on Prime Γ-Near Rings

Γ-near- ring

generalized Γ-Derivation

(σ

τ)- DerivationonΓ- ring

Jordan derivation on prime Γ-near ring

Ali Kareem

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In this paper, we introduce the notion of Jordan generalized Derivation on prime and then some related concepts are discussed. We also verify that every Jordan generalized Derivation is generalized Derivation when is a 2-torsionfree prime .

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Publication Date

Thu Apr 28 2022

Journal Name

Iraqi Journal Of Science

Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings

Semiprime Ring

Right (Left) Centralizer

Strong Commutativity Preserving

Amira A.

Abdulrahman H.

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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 Jul 01 2021

Journal Name

Journal Of Physics: Conference Series

Generalized Γ-n-Derivations on Prime Γ-Near-Rings

Hiba A.

Abdulrahman H.

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AbstractThe main purpose of this paper is to define generalized Γ-n-derivation, study and investigate some results of generalized Γ-n-derivation on prime Γ-near-ring G and <italic>K</italic> be a nonzero semi-group ideal of <italic>G</italic> which force G to be a commutative ring.

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(1)

Publication Date

Sun Jan 01 2023

Journal Name

Journal Of Interdisciplinary Mathematics

On maps of Γ -period 2 on prime Γ- near-rings

Hiba A.

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We present the concept of maps Γ- periodi2 on Γ -near-ring S. Our main goal is to research and explore the presence and mapping traits such as h Γ –hom anti-Γ –hom, Γ –α-derivations of Γ -periodi2 on Γ- near-rings.

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Publication Date

Fri Jan 01 2021

Journal Name

Advances In Intelligent Systems And Computing

Γ-n-Derivations on Semigroup Ideals on Prime Γ-Near-Rings

Hiba A.

Abdulrahman H.

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