Results 1 to 10 of about 60 (37)

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   +7 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, E. K. Sogutcu, H. M. Alnoghashi   +2 more
doaj   +4 more sources

Relationship Between a Homoderivation and a Semi-Derivation [PDF]

Journal of New Theory
Let $\wp$ 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
doaj   +4 more sources

Lie Ideals and Homoderivations in Semiprime Rings

Mathematics
Let 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, Zeliha Bedir, Emine Koç Sögütcü, Öznur Gölbaşı, Nadeem ur Rehman   +4 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   +2 more sources

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, A. Ageeb, A. Ghareeb   +2 more
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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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HOMODERIVATIONS ON RINGS: STRUCTURAL PROPERTIES AND CHARACTERIZATIONS

Barekeng
Research in ring theory has produced major advances, particularly in the study of derivations. A related notion is that of a homoderivation, which combines aspects of derivations and ring homomorphisms. An additive map  is called a homoderivation if ,
Desi Widiarti, Fitriani Fitriani, Ahmad Faisol   +2 more
doaj   +2 more sources

Study of homoderivations on quotient near rings satisfying certain algebraic constraints

Математичні Студії
Let $N$ be a near ring and $P$, a prime ideal of $N$. In this paper, we define the notion of $P$-homoderivation in near rings. Also, we investigate the structure of quotient near ring $N/P$ via $P$-homoderivation satisfying some specific identities ...
Emine Koç Sögütcü, Inzamam ul Huque
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HOMODERIVATIONS ON LIE RINGS

Barekeng
Let  be a set equipped with two binary operations, addition  and multiplication . The triple  is a Lie ring if its multiplication is the Lie bracket commutator defined by  for every .
Suffi Nuralesa, Galang Riki Ramadhan, Carolus Pasha Lazuardi Jituprasojo Hatmakelana, Nurul Fadhilah, Benediktus Panji Pradipta, Nikken Prima Puspita   +5 more
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