doi:10.21123/bsj.2010.7.4.1426-1431

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Publication Date

Sun Dec 05 2010

Journal Name

Baghdad Science Journal

Volume

7

Issue Number

4

DOI

10.21123/bsj.2010.7.4.1426-1431

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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.

...Show More Authors

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

Wed Jan 12 2022

Journal Name

Iraqi Journal Of Science

Jordan Permuting 3-Derivations of Prime Rings

Jordan Permuting 3-derivation

Lie ideal

Prime ring

Anwar K.

Sabreen J.

...Show More Authors

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

Wed Jul 17 2019

Journal Name

Iraqi Journal Of Science

On Commutativity of Prime and Semiprime - Rings with Reverse Derivations

Gamma ring

Î³-prime gamma ring

Î³-semiprime gamma ring

Î³-Lie ideal

k- reverse derivation

generalized k- reverse derivation

Shahed Ali

Abdulrahman H.

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Let M be a weak Nobusawa -ring and Î³ be a non-zero element of Î“. 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 Î“-ring, and Î³-homomorphism, anti-Î³-homomorphism of M. Also, we give some commutattivity conditions on Î³-prime Î“-ring and Î³-semiprime Î“-ring .

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(5)

(1)

Publication Date

Wed Oct 28 2020

Journal Name

Iraqi Journal Of Science

Jordan Triple Higher (Ïƒ,Ï„)-Homomorphisms on Prime Rings

Jordan homomorphisms

triple homomorphism

Jordan triple higher (Ïƒ

Ï„)- homomorphism

Salah M.

Neshtiman N.

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In this paper, the concept of Jordan triple higher -homomorphisms on prime

rings is introduced. A result of Herstein is extended on this concept from the ring into the prime ring . We prove that every Jordan triple higher -homomorphism of ring into prime ring is either triple higher -homomorphism or triple higher -anti-homomorphism of into .

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(4)

(1)

Publication Date

Sat Dec 30 2023

Journal Name

Iraqi Journal Of Science

Lie and Jordan Structure in Prime Γ- rings with Γ-centralizing Derivations

Prime Γ-ring

Lie ideal

Jordan ideal

Γ- centralizing

Derivation.

Abdulrahman

Aliaa

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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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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 Jul 01 2021

Journal Name

Iraqi Journal Of Science

Some Identities of 3-Prime Near-Rings Involving Jordan Ideals and Left Generalized Derivations

3-prime near-rings

Jordan ideals

Generalized derivations

Adel

Abdelkarim

Enaam

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In the current paper, we study the structure of Jordan ideals of a 3-prime near-ring which satisfies some algebraic identities involving left generalized derivations and right centralizers. The limitations imposed in the hypothesis were justified by examples.

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(2)

Publication Date

Sun Sep 29 2019

Journal Name

Iraqi Journal Of Science

Dependent Element and Free Actions of Centralizer and Reverse Centralizer on Prime and Semiprime Semirings

Prime semiring

Semiprime semiring

Dependent element

Free actions

Centralizer

Reverse centralizer

Maryam K.

Abdulrahman H.

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This paper develops the work of Mary Florence et.al. on centralizer of semiprime semirings and presents reverse centralizer of semirings with several propositions and lemmas. Also introduces the notion of dependent element and free actions on semirings with some results of free action of centralizer and reverse centralizer on semiprime semirings and some another mappings.

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(2)

(1)

Publication Date

Thu Mar 30 2023

Journal Name

Iraqi Journal Of Science

On (m,n) (U,R) – Centralizers

Prime ring

Semiprime ring

Left (right) Centralizer

Left(right) Jordan Centalizer

(m

n)-Jordan Centralizer

Left(righ)(m

n)(U

R)-Centralizer

(m

n)(U

R)-Centalizer

Abdulrahmam

Haneen

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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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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

Sun Jun 01 2014

Journal Name

Baghdad Science Journal

On Higher N-Derivation Of Prime Rings

derivation

Jordan ideal

higher derivation

prime ring.

Anwar K.

Abdulrahman H.

...Show More Authors

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

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