Original scientific paper
https://doi.org/10.21857/y26kec3379
Characterizations of *-Lie derivable mappings on prime *-rings
Ahmad N. Alkenani
; Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
Mohammad Ashraf
; Department of Mathematics, Aligarh Muslim University, Aligarh,202002, India
Bilal Ahmad Wani
; Department of Mathematics, Aligarh Muslim University, Aligarh,202002, India
Abstract
Let R be a *-ring containing a nontrivial self-adjoint idempotent. In this paper it is shown that under some mild conditions on R, if a mapping d : R → R satisfies
d([U*, V]) = [d(U)*, V] + [U*, d(V)]
for all U, V ∈ R, then there exists ZU,V ∈ Z(R) (depending on U and V), where Z(R) is the center of R, such that d(U + V) = d(U) + d(V) + ZU,V. Moreover, if R is a 2-torsion free prime *-ring additionally, then d = ψ + ξ, where ψ is an additive *-derivation of R into its central closure T and ξ is a mapping from R into its extended centroid C such that ξ(U + V) = ξ(U) + ξ(V) + ZU,V and ξ([U, V]) = 0 for all U, V ∈ R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras.
Keywords
Prime rings; Lie derivable mappings; involution; extended centroid; central closure.
Hrčak ID:
225229
URI
Publication date:
17.9.2019.
Visits: 1.597 *