Preferred Language
Articles
/
bsj-2354
Notes on Traces of a Symmetric Generalized (?, ?)-Biderivations and Commutativity in Prime Rings
...Show More Authors

Let R be a 2-torision free prime ring and ?, ?? Aut(R). Furthermore, G: R×R?R is a symmetric generalized (?, ?)-Biderivation associated with a nonzero (?, ?)-Biderivation D. In this paper some certain identities are presented satisfying by the traces of G and D on an ideal of R which forces R to be commutative

Scopus Crossref
View Publication Preview PDF
Quick Preview PDF
Publication Date
Thu Sep 30 2021
Journal Name
Iraqi Journal Of Science
Commutativity Results for Multiplicative (Generalized) (α,β) Reverse Derivations on Prime Rings
...Show More Authors

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  

View Publication Preview PDF
Scopus (2)
Crossref (1)
Scopus Crossref
Publication Date
Sun Mar 06 2016
Journal Name
Baghdad Science Journal
On (σ,τ)-Derivations and Commutativity of Prime and Semi prime Γ-rings
...Show More Authors

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.

View Publication Preview PDF
Crossref
Publication Date
Wed Jul 17 2019
Journal Name
Iraqi Journal Of Science
On Commutativity of Prime and Semiprime - Rings with Reverse Derivations
...Show More Authors

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 .

View Publication Preview PDF
Scopus (5)
Crossref (1)
Scopus Crossref
Publication Date
Wed Aug 31 2022
Journal Name
Iraqi Journal Of Science
Generalized Commuting Mapping in Prime and Semiprime Rings
...Show More Authors

     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.

View Publication Preview PDF
Scopus Crossref
Publication Date
Thu Apr 28 2022
Journal Name
Iraqi Journal Of Science
Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings
...Show More Authors

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 .

View Publication Preview PDF
Publication Date
Mon Oct 28 2019
Journal Name
Iraqi Journal Of Science
Generalized Strong Commutativity Preserving Centralizers of Semiprime Γ- Rings
...Show More Authors

     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.

View Publication Preview PDF
Scopus (3)
Scopus Crossref
Publication Date
Sun Apr 29 2018
Journal Name
Iraqi Journal Of Science
Orthogonal Generalized Symmetric Higher bi-Derivations on Semiprime Г-Rings .
...Show More Authors

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.

View Publication Preview PDF
Publication Date
Wed Feb 16 2022
Journal Name
Iraqi Journal Of Science
Generalized Permuting 3-Derivations of Prime Rings
...Show More Authors

This work generalizes Park and Jung's results by introducing the concept of generalized permuting 3-derivation on Lie ideal.

View Publication Preview PDF
Publication Date
Sun May 30 2021
Journal Name
Iraqi Journal Of Science
SOME RESULTS ABOUT GENERALIZED SEMIDERIVATIONS IN 3-PRIME NEAR-RINGS
...Show More Authors

   The purpose of this paper is to extend some results concerning generalized derivations to generalized semiderivations of 3-prime near rings.

View Publication Preview PDF
Scopus Crossref
Publication Date
Tue Feb 28 2023
Journal Name
Iraqi Journal Of Science
Orthogonal Generalized Higher k-Derivation on Semi Prime Г-Rings
...Show More Authors

The definition of orthogonal generalized higher k-derivation is examined in this paper and we introduced some of its related results.

View Publication Preview PDF
Scopus Crossref