Let R be a 2-torsion free prime ring with center Z(R), J be a nonzero Jordan ideal also a subring of R, and F be a generalized derivation with associated derivation d. In the present paper, we shall show that J\subseteq Z(R) if any one of the following properties holds: (i) [F(u), u]\in Z(R), (ii) F(u)u = ud(u), (iii) d(u^2)=2F(u)u, (iv) F(u^2)-2uF(u) = d(u^2)-2ud(u), (v) F^2(u)+3d^2(u)=2Fd(u)+2dF(u), (vi) F(u^2) = 2uF(u) for all u \in J.
Prime rings, Jordan ideals, generalized derivations, derivations
EL-SOUFI, MAHMOUD and ABOUBAKR, AHMED
"Generalized derivations on Jordan ideals in prime rings,"
Turkish Journal of Mathematics: Vol. 38:
2, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss2/5