Results 71 to 80 of about 184 (133)

On Additivity and Multiplicativity of Centrally Extended (α, β)‐Higher Derivations in Rings

International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.
In this paper, the concept of centrally extended (α, β)‐higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended (α, β)‐higher derivation is an (α, β)‐higher derivation.
O. H. Ezzat, Attila Gil nyi
wiley   +1 more source

A remark on centralizers in semiprime rings

Glasnik matematički, 2004
The purpose of this paper is to prove the following result: Let m 1, n 1 be fixed integers and let R be a (m + n + 2)!-torsion free semiprime ring with the identity element. Suppose there exists an additive mapping T : R R, such that T(xm+n+1) = xm T(x) xn holds for all x R. In this case T is a centralizer.
openaire   +3 more sources

Left centralizers on rings that are not semiprime

Rocky Mountain Journal of Mathematics, 2011
In any ring \(R\), an additive \(T\colon R\to R\) is a (left) centralizer on \(R\) if \(T(xy)=T(x)y\) for all \(x,y\in R\), and is a Jordan centralizer when \(T(xy+yx)=T(x)y+T(y)x\). The main result of the paper is that for any Jordan centralizer \(T\) of \(R\), if \(I\) is the \(T\)-invariant ideal of \(R\) generated by \(\{T(xy)-T(x)y\mid x,y\in R\}\)
Hentzel, Irvin, El-Sayiad, M.S.
openaire   +3 more sources

On Jordan Triple α-*Centralizers Of Semiprime Rings

Demonstratio Mathematica, 2014
Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R→R is called a left (resp. right) Jordan α-*centralizer associated with a function α: R→R if T(x2)=T(x)α(x*) (resp. T(x2)=α(x*)T(x)) holds for all x ∊ R.
Ashraf Mohammad, Mozumder Muzibur Rahman, Khan Almas   +2 more
doaj   +1 more source

Hyperideal theory in ordered Krasner hyperrings

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In this paper, we study some properties of ordered Krasner hyper-rings. Also we state some definitions and basic facts and prove some results on ordered Krasner hyperring (R, +, ·, ≤).
Omidi Saber, Davvaz Bijan
doaj   +1 more source

Soft Substructures in Quantales and Their Approximations Based on Soft Relations. [PDF]

Comput Intell Neurosci, 2022
Zhou H, Qurashi SM, Rehman MU, Shabir M, Kanwal RS, Khalil AM.   +5 more
europepmc   +1 more source

A note on semiprime rings with derivation

International Journal of Mathematics and Mathematical Sciences, 1997
Let R be a 2-torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D:R→R a derivation. If d[x,y]+[x,y]∈Z or d[x,y]−[x,y]∈Z for all x, y∈I, then R is commutative.
Motoshi Hongan
doaj   +1 more source

On functional identities involving n-derivations in rings [PDF]

Journal of Mahani Mathematical Research
In this paper, we explore various properties associated with the traces of permuting $n$-derivations satisfying certain functional identities that operate on a Lie ideal within prime and semiprime rings.
Vaishali Varshney, Shakir Ali, Naira Noor Rafiquee, Kok Wong   +3 more
doaj   +1 more source

On the structure of semiprime rings [PDF]

Proceedings of the American Mathematical Society, 1973
The structure of prime rings has recently been studied by A. W. Goldie, R. E. Johnson, L. Lesieur and R. Croisot. In their main results some sort of finiteness assumption is invariably made. It is shown in this paper that certain semiprime rings are subdirect sums of full rings of linear transformations of a right vector space over
openaire   +1 more source

Fuzzy bipolar soft semiprime ideals in ordered semigroups. [PDF]

Heliyon, 2021
Aziz-Ul-Hakim, Khan H, Ahmad I, Khan A.
europepmc   +1 more source