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

Document Type : Research Paper


Department of Mathematics Aligarh Muslim University, Aligarh, India


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: $(i)\delta(x)\delta(y)\mp x\circ y\in Z(\Re),$ $(ii)[x,y]-\delta(xy)\delta(yx)\in Z(\Re),$ $(iii)\delta(x)\circ \delta(y)\mp [x,y]\in Z(\Re),$ $(iv)\delta(x)\circ \delta(y)\mp xy\in Z(\Re),$ $(v) \delta(x)\delta(y)\mp yx\in Z(\Re),$ where $\delta$ is the trace of $n$-additive map $\digamma: \underbrace{\Re\times \Re\times....\times \Re}_{n-times}\longrightarrow \Re$,$~\mbox{for all}~ x,y\in U$.