Results 1 to 10 of about 72 (43)
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 Hx+y−Hx−Hy∈Zℜ and Hxy−HxHy−Hxαy−αxHy∈Zℜ for any x,y∈ℜ) where α is a mapping of ℜ and discuss the relationship between ...
Mahmoud M. El-Soufi, A. Ghareeb
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Results on Lie ideals of prime ringswith homoderivations [PDF]
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 [PDF]
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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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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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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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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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
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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 +2 more
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