On Jordan and Jordan higher derivable maps of rings
Bull. Korean Math. Soc.
Published online October 16, 2019
Lei Liu
Xidian University
Abstract : Let R be a 2-torsion free unital ring containing a non-trivial idempotent. An
additive map δ from R into itself is called a Jordan derivable map at commutative zero point
if δ(AB + BA) = δ(A)B + Bδ(A) + Aδ(B) + δ(B)A for all A,B ∈ R with AB = BA = 0.
In this paper, we prove that, under some mild conditions, each Jordan derivable map at
commutative zero point has the form δ(A) = ψ(A) + CA for all A ∈ R, where ψ is an
additive Jordan derivation of R and C is a central element of R. Then we generalize the
result to the case of Jordan higher derivable maps at commutative zero point. These results
are also applied to some operator algebras.
Keywords : Derivations; Jordan derivable maps; Jordan higher derivable maps; Commutative zero points
MSC numbers : 16W25; 47B47
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