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bsj-2623
On Higher N-Derivation Of Prime Rings
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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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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
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Publication Date
Sun Mar 06 2016
Journal Name
Baghdad Science Journal
On (σ,τ)-Derivations and Commutativity of Prime and Semi prime Γ-rings
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Let R be a Г-ring, and σ, τ be two automorphisms of R. An additive mapping d from a Γ-ring R into itself is called a (σ,τ)-derivation on R if d(aαb) = d(a)α σ(b) + τ(a)αd(b), holds for all a,b ∈R and α∈Γ. d is called strong commutativity preserving (SCP) on R if [d(a), d(b)]α = [a,b]α(σ,τ) holds for all a,b∈R and α∈Γ. In this paper, we investigate the commutativity of R by the strong commutativity preserving (σ,τ)-derivation d satisfied some properties, when R is prime and semi prime Г-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
Sun Jul 02 2023
Journal Name
Iraqi Journal Of Science
Nilpotency of Centralizers in Prime Rings
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Nilpotency of Centralizers in Prime 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
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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
Wed Feb 16 2022
Journal Name
Iraqi Journal Of Science
Generalized Permuting 3-Derivations of Prime Rings
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This work generalizes Park and Jung's results by introducing the concept of generalized permuting 3-derivation on Lie ideal.

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Publication Date
Sun Sep 04 2011
Journal Name
Baghdad Science Journal
Jordan left (?,?) -derivations Of ?-prime rings
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It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

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Publication Date
Sat Dec 30 2023
Journal Name
Iraqi Journal Of Science
Derivable Maps of Prime Rings
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Our active aim in this paper is to prove the following Let Ŕ be a ring having an
idempotent element e(e  0,e 1) . Suppose that R is a subring of Ŕ which
satisfies:
(i) eR  R and Re  R .
(ii) xR  0 implies x  0 .
(iii ) eRx  0 implies x  0( and hence Rx  0 implies x  0) .
(iv) exeR(1 e)  0 implies exe  0 .
If D is a derivable map of R satisfying D(R )  R ;i, j 1,2. ij ij Then D is
additive. This extend Daif's result to the case R need not contain any non-zero
idempotent element.

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Publication Date
Mon Jan 10 2022
Journal Name
Iraqi Journal Of Science
Centralizers on Prime and Semiprime Γ-rings
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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
Fri Mar 27 2020
Journal Name
Iraqi Journal Of Science
Γ-(,δ)-Derivation on Semi-Group Ideals in Prime Γ-Near-Ring: -(,δ)-derivations on Semi-group Ideals in Prime -
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The main purpose of this paper is to investigate some results. When h is  -( ,δ) – Derivation on prime Γ-near-ring G and K is a nonzero semi-group ideal of G, then G is commutative .

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