Mehsin Jabel Atteya, Department of Mathematics, Al-Mustansiriyah University, College of Education, Baghdad, Iraq.
The main purpose of this paper is studying and investigating some results concerning a symmetric bi-derivation D:R×R→R and d the trace of D ,on prime rings and semiprime rings R, where R admits for a symmetric bi-derivation D satisfying some conditions on R, (i). ([d(x),x]) n =0 for all x ∈R. (ii). D1 (d2 (x),x) n=0 holds for all x ∈R. (iii). (d1 (d2 (x))- f(x)) n=0 holds for all x ∈R. Where n be a positive integer and R be a 2-torsion and 3-torsion free.
Symmetric Bi-derivation, Derivation, Central Mapping, Semiprime Rings, Prime Ring, Torsion Free
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