Annihilator condition on power values of commutators with derivations
Received:April 24, 2018  Revised:August 07, 2018
Key Word: Prime ring, derivation, extended centroid.
Fund ProjectL:
 Author Name Affiliation E-mail Shuliang Huang School of Mathematics and Finance,Chuzhou University shulianghuang@sina.com
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Let $R$ be a prime ring with center $Z(R)$, $I$ a nonzero ideal of $R$, $d$ a nonzero derivation of $R$ and $0\neq a\in R$. In the present paper, our object is to study the situation $a[d(x^k),x^k]^n\in Z(R)$ for all $x \in I$ under certain conditions, where $n(\geq 1), k(\geq 1)$ are fixed integers