Results 21 to 30 of about 117 (54)
On nilpotent homoderivations in semi-prime rings
Boletim da Sociedade Paranaense de MatemáticaLet $R$ 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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Quotient near-rings involving P -homoderivations
Annals of the Alexandru Ioan Cuza University - MathematicsLet 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
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Relationship Between a Homoderivation and a Semi-Derivation
Journal of New TheoryLet $\wp$ be a ring. It is shown that if an additive mapping $\vartheta$ is a zero-power valued on $\wp$, then $\alpha:\wp\rightarrow\wp$ such that $\alpha=\vartheta+1$ is a bijective mapping of $\wp.$ The main aim of this study is to prove that $\vartheta$ is a homoderivation of $\wp$ if and only if $\vartheta:\wp\rightarrow\wp$ such that $\vartheta ...
Selin Türkmen
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Homoderivations and Jordan right ideals in 3-prime near-rings
AIP Conference Proceedings, 2019 Abdelkarim Boua
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Characterization of the center of a prime Banach algebra by its homoderivations
Boletim da Sociedade Paranaense de MatemáticaLet 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
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On centrally-extended $ n $-homoderivations on rings
AIMS MathematicsIn 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
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On Square-Closed Lie Ideals and Generalized Homoderivations in Prime Rings
Integra: Journal of Integrated Mathematics and Computer ScienceLet M be a square-closed noncentral Lie ideal of a prime ring R with char(R) ≠ 2. An additive mapping G on R is defined as a generalized homoderivation if it satisfies G(στ) = G(σ) h(τ) + G′(σ) y + x h(τ) for all σ and τ in R. This paper focuses on studying generalized homoderivations of prime rings using square-closed Lie ideals that satisfy certain ...
null G. Naga Malleswari +1 more
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Remarks on the notion of homo-derivations [PDF]
, 2020 The purpose of this paper is to study the (different) notions of homo-derivations. These are additive mappings f of a ring R that also fulfill the identity f(xy)=f(x)y+xf(y)+f(x)f(y)(x,y∈R), or (in case of the other notion) the system of equations f ...
Gselmann, Eszter, Kiss, Gergely
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NIL DERIVATIONS AND d-IDEALS ON POLYNOMIAL RINGS [PDF]
Let be a ring. An additive mapping is called derivation if satisfies Leibniz's rule, i.e., for every In a special case, for each there exists a positive integer which depends on such that , then
Faisol, Ahmad +3 more
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On centrally-extended Jordan endomorophisms in rings
, 2023 The aim of this article is to introduce the concept of centrally-extended Jordan endomorphisms and proving that if $R$ is a non-commutative prime ring of characteristic not two, and $G$ is a CE- Jordan epimorphism such that $[G(x), x] \in Z(R)$ ($[G(x ...
Gouda, Aziza, Nabiel, H.
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