Results 11 to 20 of about 65 (46)

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
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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
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On zero-power valued homoderivations in 3-prime near-rings

Boletim da Sociedade Paranaense de Matemática, 2022
We will start this article by proving a crucial concept, which will allow us to overcome a set of obstacles we encountered in previous articles concerning the commutativity of near-ring involving homoderivations and Jordan ideals. Furthermore, we present examples to show that limitations imposed in the hypothesis of our results are necessary.
Adel En-guady, Samir Mouhssine, Abdelkarim Boua   +2 more
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Reverse Homoderivations on (Semi)-prime Rings

Journal of the Indonesian Mathematical Society
In this paper, we explore and examine a new class of maps known as reverse homoderivations. A reverse homoderivation refers to an additive map g defined on a ring T that satisfies the condition, g(ϑℓ)=g(ℓ)g(ϑ)+g(ℓ)ϑ+ℓg(ϑ), for all ϑ,ℓ∈T. We present various results that enhance our understanding of reverse homoderivations, including their existence in ...
Shakir Ali, Naira Noor Rafiquee, Vaishali Varshney, Outdom Dy   +3 more
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Additivity and Central Behavior of CE‐Generalized Homoderivations in Associative Rings

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study examines the commutativity of a ring R endowed with a special class of mappings termed centrally extended generalized homoderivations. These mappings serve as an extension of several existing concepts, including homoderivations, generalized homoderivations, and left centralizers.
Hicham Saber, Hafedh Alnoghashi, Radwan M. Al-Omary, Khaled Aldwoah, Bakri Younis, M. I. Elashiry, Huadong Su   +6 more
wiley   +1 more source

Homoderivations and Their Impact on Lie Ideals in Prime Rings

Natural and Applied Sciences Journal, 2023
Assume we have a prime ring denoted as $R$, with a characteristic distinct from two. The concept of a homoderivation refers to an additive map $Η$ of a ring $R$ that satisfies the property $Η(r_1 r_2 )=Η(r_1 ) r_2+r_1 Η(r_2 )+Η(r_1 )Η(r_2 )$, $\forall r_1,r_2 \in R$.
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On Additivity and Multiplicativity of Centrally Extended (α, β)‐Higher Derivations in Rings

International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.
In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation.
O. H. Ezzat, Attila Gil nyi
wiley   +1 more source

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
Mahmoud M. EL-Soufi, Munerah Almulhem, M. S. Tammam EL-Sayiad   +2 more
openaire   +1 more source

On nilpotent homoderivations in semi-prime rings

Boletim da Sociedade Paranaense de Matemática
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
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On centrally-extended $ n $-homoderivations on rings

AIMS Mathematics
In this article, we explored the commutativity of a ring $ \Lambda $ that is equipped with a unique class of mappings called centrally extended $ n $-homoderivations, where $ n $ is an integer. These mappings generalize the concepts of derivations and homoderivations. Furthermore, we investigated specific properties of the center of such rings.
M. S. Tammam El-Sayiad, Munerah Almulhem
openaire   +2 more sources