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 $Re$ $neq$ $(2^{n}-2)$ is central, if one of the following holds: $(i)delta(x)delta(y)mp xcirc yin Z(Re),$ $(ii)[x,y]-delta(xy)delta(yx)in Z(Re),$ $(iii)delta(x)circ delta(y)mp [x,y]in Z(Re),$ $(iv)delta(x)circ delta(y)mp xyin Z(Re),$ $(v) delta(x)delta(y)mp yxin Z(Re),$ where $delta$ is the trace of $n$-additive map $digamma: underbrace{Retimes Retimes....times Re}_{n-times}longrightarrow Re$,$~mbox{for all}~ x,yin U$.