Results 1 to 10 of about 117 (54)
Centrally Extended α-Homoderivations on Prime and Semiprime Rings [PDF]
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
doaj +7 more sources
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
doaj +9 more sources
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
doaj +7 more sources
Centralizing n-Homoderivations of Semiprime Rings [PDF]
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
doaj +4 more sources
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
doaj +6 more sources
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
doaj +6 more sources
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
doaj +5 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
core +5 more sources
SEMIPRIME IDEALS AND P−COMMUTING HOMODERIVATIONS ON IDEALS [PDF]
Facta Universitatis, Series: Mathematics and InformaticsThe 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.
Bedir, Zeliha
core +4 more sources
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 +2 more
core +5 more sources