Results 1 to 10 of about 61 (49)
Centralizing n-Homoderivations of Semiprime Rings
Journal of Mathematics, 2022 We introduce the notion of n-homoderivation on a ring ℜ and show that a semiprime ring ℜ must have a nontrivial central ideal if it admits an appropriate n-homoderivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses,
M. S. Tammam El-Sayiad +2 more
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On generalized homoderivations of prime rings
Математичні Студії, 2023 Let $\mathscr{A}$ be a ring with its center $\mathscr{Z}(\mathscr{A}).$ An additive mapping $\xi\colon \mathscr{A}\to \mathscr{A}$ is called a homoderivation on $\mathscr{A}$ if $\forall\ a,b\in \mathscr{A}\colon\quad \xi(ab)=\xi(a)\xi(b)+\xi(a)b+a\xi(
N. Rehman +2 more
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Results on Lie ideals of prime ringswith homoderivations
Extracta Mathematicae, 2023 Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping Hon R is called a homoderivation if H(xy) =H(x)H(y)+H(x)y+xH(y)for all x, y∈R. In this paper we investigate homoderivations satisfying
A. Sarikaya, O. Gölbasi
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Homoderivations in Prime Rings
Journal of New Theory, 2023 The study consists of two parts. The first part shows that if $h_{1}(x)h_{2}(y)=h_{3}(x)h_{4}(y)$, for all $x,y\in R$, then $ h_{1}=h_{3}$ and $h_{2}=h_{4}$. Here, $h_{1},h_{2},h_{3},$ and $h_{4}$ are zero-power valued non-zero homoderivations of a prime
Neşet Aydın, Ayşe Engin
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A Characterization of Semiprime Rings with Homoderivations
Journal of New Theory, 2023 This paper is focused on the commutativity of the laws of semiprime rings, which satisfy some algebraic identities involving homoderivations on ideals. It provides new and notable results that will interest researchers in this field, such as “R contains ...
Emine Koç Sögütcü
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Centrally Extended α‐Homoderivations on Prime and Semiprime Rings
Journal of Mathematics, 2022 We present a new type of mappings called centrally extended α‐homoderivations of a ring ℜ (i.e., a map H from ℜ into ℜ which satisfies H(x + y) − H(x) − H(y) ∈ Z(ℜ) and H(xy) − H(x)H(y) − H(x)α(y) − α(x)H(y) ∈ Z(ℜ) for any x, y ∈ ℜ) where α is a mapping of ℜ and discuss the relationship between these mappings and other related mappings.
Mahmoud M. El-Soufi, A. Ghareeb
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Prime Ideals and Homoderivations on Rings
Cumhuriyet Science JournalIn this paper, we aim to establish a new approach that involves characterizing the commutativity of a quotient ring L/P with homoderivations of L satisfying some algebraic identities involving the prime ideal P.
Zeliha Bedir
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Lie Ideals and Homoderivations in Semiprime Rings
MathematicsLet S be a 2-torsion free semiprime ring and U be a noncentral square-closed Lie ideal of S. An additive mapping ℏ on S is defined as a homoderivation if ℏ(ab)=ℏ(a)ℏ(b)+ℏ(a)b+aℏ(a) for all a,b∈S. In the present paper, we shall prove that ℏ is a commuting
Ali Yahya Hummdi +4 more
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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 ...
Selin Türkmen
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Additivity and Central Behavior of CE‐Generalized Homoderivations in Associative Rings
Journal of MathematicsThis study examines the commutativity of a ring 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 +5 more
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