2011 / September Volume 6 No.3
Generalized Skew Derivations With Engel Conditions On Lie Ideals
| Published Date |
2011 / September
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|---|---|
| Title | Generalized Skew Derivations With Engel Conditions On Lie Ideals |
| Author | |
| Keyword | |
| Download | |
| Pagination | 305-320 |
| Abstract | Let $R$ be a prime
ring and $L$ a noncommutative Lie ideal of $R$. Suppose that $f$ is
a nonzero right generalized $\beta$-derivation of $R$ associated
with a $\beta$-derivation $\delta$ such that $[f(x),x]_k=0$ for all $x\in L$, where $k$ is a fixed positive integer. Then either there
exists $s\in C$ scuh that $f(x)=sx$ for all $x\in R$ or $R\subseteq M_2(F)$ for some field $F$. Moreover, if the latter case holds, then either ${\rm char} R= 2$ or ${\rm char}R\ne 2$ and $f(x)=bx-xc$ for all $x\in R$, where $b,c\in\mathop{_{\mathscr F}\hspace{-0.3mm}R}$ and $b+c\in C$.
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| AMS Subject Classification |
16W20, 16W25, 16W55
|
| Received |
2011-07-26
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| Accepted |
2011-07-20
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