Generalized derivations on Jordan ideals in prime rings

Authors : Mahmmoud EL-SOUFI, Ahmed ABOUBAKR

Pages : 233-239

Doi:10.3906/mat-1211-42

View : 11 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let R be a 2-torsion free prime ring with center Zinsert ignore into journalissuearticles values(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 Zinsert ignore into journalissuearticles values(R); if any one of the following properties holds: insert ignore into journalissuearticles values(i); [Finsert ignore into journalissuearticles values(u);, u]\in Zinsert ignore into journalissuearticles values(R);, insert ignore into journalissuearticles values(ii); Finsert ignore into journalissuearticles values(u);u = udinsert ignore into journalissuearticles values(u);, insert ignore into journalissuearticles values(iii); dinsert ignore into journalissuearticles values(u2);=2Finsert ignore into journalissuearticles values(u);u, insert ignore into journalissuearticles values(iv); Finsert ignore into journalissuearticles values(u2);-2uFinsert ignore into journalissuearticles values(u); = dinsert ignore into journalissuearticles values(u2);-2udinsert ignore into journalissuearticles values(u);, insert ignore into journalissuearticles values(v); F2insert ignore into journalissuearticles values(u);+3d2insert ignore into journalissuearticles values(u);=2Fdinsert ignore into journalissuearticles values(u);+2dFinsert ignore into journalissuearticles values(u);, insert ignore into journalissuearticles values(vi); Finsert ignore into journalissuearticles values(u2); = 2uFinsert ignore into journalissuearticles values(u); for all u \in J.
Keywords : Prime rings, Jordan ideals, generalized derivations, derivations