An Identity on Partial Generalized Automorphisms of Prime Rings

Abstract

Let $R$ be a prime ring with center $Z(R)$, $T:R⟶R$ be a non-zero partial generalized automorphism of $R$, $L$ a Lie ideal of $R$, $s\ge 0,t\ge 0$ and $n\ge 1$ fixed integers, such that $(u^s(T(u)\circ u)u^t{)}^n=0$ for all $u\in L$. If either Char$(R)>n+1$ or Char$(R)=0$, then $L\subseteq Z(R)$.