On generalized derivations and Jordan ideals of prime rings (Q2024406)

One of the fundamental concepts of the development of ring theory is the structure prime rings. A ring \(R\) is called a prime ring if \(IK=\{0\}\) implies \(I=\{0\}\) or \(K=\{0\}\) for any ideals \(I,K\) of \(A\). Moreover, a generalization of derivations on Jordan ideals in prime ring has previously been studied intensively by \textit{M. El-Soufi} and \textit{A. Aboubakr} [Turk. J. Math. 38, No. 2, 233--239 (2014; Zbl 1292.16035)] in their paper in 2014. In this paper, the authors show that all theorems discovered by Soufi and Aboubakr [loc. cit.] are also valid for Jordan ideals which are not necessary subrings.