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- W1639508072 abstract "Let $R$ be a semiprime ring with a derivation $d$ and let $U$ be a Lie ideal of $R$, $ain R$. Suppose that $ad(u)^n=0$ for all $uin U$, where $n$ is a fixed positive integer. Then $ad(I)=0$ for $I$ the ideal of $R$ generated by $[U,U]$ and if $R$ is 2-torsion free, then $ad(U)=0$. Furthermore, $R$ is a subdirect sum of semiprime homomorphic images $R_1$ and $R_2$ with derivations $d_1$ and $d_2$, induced canonically by $d$, respectively such that $overline ad_1(R_1)=0$ and the image of $U$ in $R_2$ is commutative (central if $R$ is 2-torsion free), where $overline a$ denotes the image of $a$ in $R_1$. Moreover, if $U=R$, then $ad(R)=0$. This gives BresÌarâs theorem without the $(n-1)!$-torsion free assumption on $R$." @default.
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- W1639508072 date "1996-01-01" @default.
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- W1639508072 title "A result on derivations" @default.
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