Traces of permuting n-additive mappings in *-prime rings

In this paper, we prove that a nonzero square closed *-Lie ideal U of a *-prime ring \Re of Char \Re \neq (۲^{n}-۲) is central, if one of the following holds: (i)\delta(x)\delta(y)\mp x\circ y\in Z(\Re), (ii)[x,y]-\delta(xy)\delta(yx)\in Z(\Re), (iii)\delta(x)\circ \delta(y)\mp [x,y]\in Z(\Re), (iv)\delta(x)\circ \delta(y)\mp xy\in Z(\Re), (v) \delta(x)\delta(y)\mp yx\in Z(\Re), where \delta is the trace of n-additive map \digamma: \underbrace{\Re\times \Re\times....\times \Re}_{n-times}\longrightarrow \Re,~\mbox{for all}~ x,y\in U.

Keywords:

Prime rings , *-prime rings , *-Lie ideals , Trace of n-additive maps