Geodesic
Annihilators of skew derivations with Engel conditions on prime rings
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 587-603
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Let $R$ be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring $Q$, $C$ the extended centroid of $R$ and $a\in R$. Suppose that $\delta $ is a nonzero $\sigma $-derivation of $R$ such that $a[\delta (x^{n}),x^{n}]_{k}=0$ for all $x\in R$, where $\sigma $ is an automorphism of $R$, $n$ and $k$ are fixed positive integers. Then $a=0$.
Let $R$ be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring $Q$, $C$ the extended centroid of $R$ and $a\in R$. Suppose that $\delta $ is a nonzero $\sigma $-derivation of $R$ such that $a[\delta (x^{n}),x^{n}]_{k}=0$ for all $x\in R$, where $\sigma $ is an automorphism of $R$, $n$ and $k$ are fixed positive integers. Then $a=0$.
DOI : 10.21136/CMJ.2019.0412-18
Classification : 16W20, 16W25
Keywords: prime ring; derivation; skew derivation; automorphism 
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Pehlivan, Taylan; Albas, Emine. Annihilators of skew derivations with Engel conditions on prime rings. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 587-603. doi: 10.21136/CMJ.2019.0412-18

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