A note on Jordan triple higher *-derivations on semiprime rings.
Let \(R\) be a 6-torsion free semiprime ring with involution *. The author extends the definitions of Jordan higher derivation and Jordan triple higher derivation to rings with involution. Let \(D=(d_n)\) for \(n\geq 0\) be a sequence of additive maps of \(R\) with \(d_0=\text{id}_R\). Then \(D\) is a Jordan higher *-derivation of \(R\) when for any \(n\geq 1\) and all \(x\in R\), \(d_n(x^2)=\sum_{i+j=n}d_i(x)d_j(x^{*^i})\), and \(D\) is a Jordan triple higher *-derivation of \(R\) when for any \(n\geq 1\) and all \(x,y\in R\), \(d_n(xyx)=\sum_{i+j+k=n}d_i(x)d_j(y^{*^i})d_k(x^{*^{i+j}})\). The main results of the paper show that \(D\) is a Jordan higher *-derivation of \(R\) if and only if \(D\) is a Jordan triple higher *-derivation of \(R\).
scientific article; zbMATH DE number 6304836
scientific article