Rad HAZU, Matematičke znanosti, Vol. 23 (2019), 51-69.

CHARACTERIZATIONS OF *-LIE DERIVABLE MAPPINGS ON PRIME *-RINGS

Ahmad N. Alkenani, Mohammad Ashraf and Bilal Ahmad Wani

Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
e-mail: aalkenani10@hotmail.com

Department of Mathematics, Aligarh Muslim University, Aligarh,202002, India
e-mail: mashraf80@hotmail.com
e-mail: bilalwanikmr@gmail.com

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.

2010 Mathematics Subject Classification.   16N60, 16W25, 16W10.

Key words and phrases.   Prime rings, Lie derivable mappings, involution, extended centroid, central closure.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/y26kec3379

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