Abstract
Let R be a ring and \({\mathbb{N}}\) be the set of all non-negative integers. A family of maps \({D=\{d_n\}_{n \in \mathbb{N}}}\) is said to be Jordan triple higher derivable if \({d_n(aba)=\sum \nolimits_{p+q+r=n} d_p(a)d_q(b)d_r(a)}\) holds for all \({a,b \in R}\), where d 0 = I R , (the identity map on R). In this paper, we determine Jordan triple higher derivable map on a ring R, which contains a nontrivial idempotent which is automatically additive. An immediate application of our main result shows that every Jordan triple higher derivable map becomes higher derivation on R.
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Ashraf, M., Parveen, N. On Jordan Triple Higher Derivable Mappings on Rings. Mediterr. J. Math. 13, 1465–1477 (2016). https://doi.org/10.1007/s00009-015-0606-3
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DOI: https://doi.org/10.1007/s00009-015-0606-3