On $\ast$-$(\sigma,\tau)$-Lie ideals of $\ast$-prime rings with derivation

Year 2018, Volume: 47 Issue: 5, 1240 - 1247, 16.10.2018

Neşet Aydın Emine Koç Öznur Gölbaşı

Abstract

Let $R$ be a $\ast$-prime ring with characteristic not 2, $U$ be a nonzero $\ast$-$(\sigma,\tau)$-Lie ideal of $R$ and $d$ be a nonzero derivation of $R$. Suppose $\sigma$, $\tau$ be two automorphisms of $R$ such that $\sigma d=d\sigma$, $\tau d=d\tau$ and $\ast$ commutes with $\sigma,\tau,d$. In the present paper it is shown that if $d^2(U)=(0)$, then $U\subset Z$.

Keywords

Derivations, $(\sigma;\tau)$-Lie Ideals, $\ast-$prime rings, involution

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