Results 1 to 10 of about 73 (46)

On $(\Phi , m)$-homoderivations in Rings

European Journal of Pure and Applied Mathematics
In this article, we examine the commutativity of a ring $\Omega$ endowed with a specific kind of mappings called centrally extended $(\Phi, m)$-homoderivations, where $\Phi$ is a mapping on $\Omega$, and $m$ is an integer.  This mapping is a comprehensive kind of the homoderivation, $\Phi- $homoderivation, and $ m $-homoderivation.  Besides, we provide
M S Tammam El-Sayiad
exaly   +2 more sources

On nilpotent homoderivations in semi-prime rings

Boletim Da Sociedade Paranaense De Matematica
Let $R$ be an associative ring and let $s \geq 1$ be a fixed integer. An additive map $h$ on $R$ is called a homoderivation if $h(xy) = h(x)h(y) + h(x)y + xh(y)$ holds for all $x, y \in R.$ In \cite{Chung83,Chung84,Luh84}, Chung and Luh proved several results about the nilpotency of derivations in semi-prime rings. Similarly, the main objective of this
Lahcen Taoufiq, Said Belkadi
exaly   +2 more sources

Quotient near-rings involving P -homoderivations

Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi - Matematica
Let N be a near-ring and P be a 3-prime ideal of N . This paper introduces a novel concept known as P-homoderivation and investigates the commutativity of the quotient near-ring N /P when N has a P-homoderivation satisfying certain distinction identities. In addition, we extend several known results related to 3-prime near-rings with homoderivations.
Abdelkarim Boua
exaly   +2 more sources

On n-anti-homoderivations of Prime and Semiprime Rings

European Journal of Pure and Applied Mathematics
We present the notion of $n$-anti-homoderivations, a novel class of additive mappings on rings. Within this framework, we establish strong necessary conditions for rings' commutativity and the presence of nontrivial central ideals. Our approach not only generalizes several classical results as special cases, but also  addresses open problems concerning
M S Tammam El-Sayiad
exaly   +2 more sources

SEMIPRIME IDEALS AND P−COMMUTING HOMODERIVATIONS ON IDEALS

Facta Universitatis Series Mathematics and Informatics
The first purpose of this article is to examine the structure of an S=Pquotient ring, where S is any ring and P is the semiprime ideal of S. More specifically,we look at differential identities in the semiprime ideal of an arbitrary ring using theP-commuting homoderivations.
exaly   +3 more sources

The commutativity of prime rings with homoderivations

International Journal of Advanced and Applied Sciences, 2018
E. F. Alharfie, N. M. Muthana
exaly   +2 more sources

Characterization of the center of a prime Banach algebra by its homoderivations

Boletim Da Sociedade Paranaense De Matematica
Let X be a Banach algebra. The value of the present article focuses on the fact that, first, it presents detailed informations about zero-power valued maps on X ,second, it provides characterization to the center of X via its homoderivations. Finally, we include some examples to show that various restrictions in the hypothesis of our theorems are not ...
Mohamed Moumen, Lahcen Taoufiq
exaly   +2 more sources

Semiprime rings with generalized homoderivations

Boletim da Sociedade Paranaense de Matemática, 2022
This study develops some results involving generalized homoderivation in semiprime rings and investigates the commutativity of semiprime rings admitting generalized homoderivations of ring R satisfying certain identities and some related results have also been discussed.
Abdelkarim Boua, Emine Koç Sögütcü
openaire   +3 more sources

Jordan homoderivation behavior of generalized derivations in prime rings

Ukrains’kyi Matematychnyi Zhurnal, 2023
UDC 512.5 Suppose that R is a prime ring with c h a r ( R ) ≠ 2 and f ( ξ 1 , … , ξ n ) is a noncentral multilinear polynomial over C ( = Z ( U ) ) , where U is the Utumi quotient ring of R .
Bera, Nripendu, Dhara, Basudeb
openaire   +1 more source

Centrally-extended homoderivations on rings

Gulf Journal of Mathematics, 2016
Let R be a ring with center Z(R). A mapping H from R into itself is called a centrally-extended homoderivation on R if for each x, y ∈ R, H(x+y) - H(x) - H(y) ∈ Z(R) and H(xy) - H(x)H(y)- H(x)y - xH(y) ∈ Z(R). We present examples of mappings that are centrally-extended homoderivations but not homoderivations.
Asmaa Melaibari, Najat Muthana, Ahmad Al-Kenani   +2 more
openaire   +1 more source