Jordan higher centralizers on semiprime rings and related mappings.
Let \(R\) be a 2-torsion free semiprime ring with \(J=(\delta_i)_{i\geq 0}\) and \(I=(\varphi_i)_{i\geq 0}\) two sequences of additive maps \(\delta_i,\varphi_j\colon R\to R\) with \(\delta_0=id_R\) and \(\varphi_0=0\). Call \(J\) a Jordan higher derivation of \(R\) if for all \(a\in R\), \(\delta_n(a^2)=\sum_{n=i+j}\delta_i(a)\delta_j(a)\), call \(I\) a higher left centralizer for \(J\) if for all \(a,b\in R\), \(\varphi_n(ab)=\sum_{n=i+j}\varphi_i(a)\delta_j(b)\), and call \(I\) a Jordan higher left centralizer for \(J\) if for all \(a\in R\), \(\varphi_n(a^2)=\sum_{n=i+j}\varphi_i(a)\delta_j(a)\).NEWLINENEWLINE The main result in the paper shows that if \(I\) is a Jordan higher left centralizer for \(J\), then \(I\) is a higher left centralizer for \(J\).
scientific article; zbMATH DE number 6362201