Let $R$ be a prime ring of characteristic $\neq 2$ with a derivation $d\neq 0$, $L$ a Lie ideal of $R$, $k,m,n$ positive integers such that $v^m[d(u),u]_kv^n=0$, for all $u,v\in L$. We prove that $L$ must be central. We also examine the case $R$ is a 2-torsion free semiprime ring and $[z,t]^m[d([x,y]),[x,y]]_k[z,t]^n=0$, for all $x,y,z,t\in R$.
A note on Sandwich Engel Conditions on Lie Ideals in Semiprime Rings
RANIA F
2013-01-01
Abstract
Let $R$ be a prime ring of characteristic $\neq 2$ with a derivation $d\neq 0$, $L$ a Lie ideal of $R$, $k,m,n$ positive integers such that $v^m[d(u),u]_kv^n=0$, for all $u,v\in L$. We prove that $L$ must be central. We also examine the case $R$ is a 2-torsion free semiprime ring and $[z,t]^m[d([x,y]),[x,y]]_k[z,t]^n=0$, for all $x,y,z,t\in R$.File in questo prodotto:
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