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On Skew Left ∗-n-Derivations of ∗-Ring
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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 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
Mon Jan 01 2024
Journal Name
2nd International Conference For Engineering Sciences And Information Technology (esit 2022): Esit2022 Conference Proceedings
Ideals of the full transformation semigroup of a free left G-act on n-generators
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Publication Date
Tue Nov 30 2021
Journal Name
Iraqi Journal Of Science
(α, β) – Derivations on Prime Inverse Semirings
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Let S be a prime inverse semiring with center Z(S). The aim of this research is to prove some results on the prime inverse semiring with (α, β) – derivation that acts as a homomorphism or as an anti- homomorphism, where α, β are automorphisms on S.

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Publication Date
Thu Jan 13 2022
Journal Name
Iraqi Journal Of Science
Examples of -Skew -Armendariz Rings
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In this paper extensive examples and related counterexamples of the category of -skew -Armendariz rings are given. This category of rings regards a new generalization for the concepts of -skew Armendariz and skew -Armendariz rings. A ring is called -skew -Armendariz if for any ( ) Σ and ( ) Σ such that ( ) ( ) ( ), then ( ) ( ) for each and . First some general properties of -skew -Armendariz rings are studied and then relations between -skew -Armendariz rings and other related rings are investigated. Also various examples of non -skew -Armendariz rings are established.

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
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
Thu Sep 30 2021
Journal Name
Iraqi Journal Of Science
Commutativity Results for Multiplicative (Generalized) (α,β) Reverse Derivations on Prime Rings
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Let  be a prime ring,  be a non-zero ideal of  and   be automorphism on. A mapping  is called a multiplicative (generalized)  reverse derivation if  where  is any map (not necessarily additive). In this paper, we proved the commutativity of a prime ring R admitting a multiplicative (generalized)  reverse derivation  satisfying any one of the properties:

 

 

 for all x, y  

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Publication Date
Thu Mar 30 2023
Journal Name
Iraqi Journal Of Science
On (m,n) (U,R) – Centralizers
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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
Sun Sep 04 2011
Journal Name
Baghdad Science Journal
Semigroup ideal in Prime Near-Rings with Derivations
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In this paper we generalize some of the results due to Bell and Mason on a near-ring N admitting a derivation D , and we will show that the body of evidence on prime near-rings with derivations have the behavior of the ring. Our purpose in this work is to explore further this ring like behavior. Also, we show that under appropriate additional hypothesis a near-ring must be a commutative ring.

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Publication Date
Sun Oct 22 2023
Journal Name
Iraqi Journal Of Science
Reverse Derivations With Invertible Values
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In this paper, we will prove the following theorem, Let R be a ring with 1 having
a reverse derivation d ≠ 0 such that, for each x R, either d(x) = 0 or d(x) is
invertible in R, then R must be one of the following: (i) a division ring D, (ii) D 2 ,
the ring of 2×2 matrices over D, (iii) D[x]/(x ) 2
where char D = 2, d (D) = 0 and
d(x) = 1 + ax for some a in the center Z of D. Furthermore, if 2R ≠ 0 then R = D 2 is
possible if and only if D does not contain all quadratic extensions of Z, the center of
D.

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