Geodesic
Derivations with power central values on Lie ideals in prime rings
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 147-153 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.
Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.
Classification : 16N60, 16R50, 16W10, 16W25
Keywords: prime ring; derivation; extended centroid; martindale quotient ring 
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Dhara, Basudeb; Sharma, R. K. Derivations with power central values on Lie ideals in prime rings. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 147-153. http://geodesic.mathdoc.fr/item/CMJ_2008_58_1_a9/

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