Annihilator Condition on Power Values of Commutators with Derivations
Received:April 24, 2018  Revised:August 29, 2018
Key Word: prime ring   derivation   extended centroid
Fund ProjectL:Supported by the Natural Science Foundation of Anhui Province (Grant Nos.1808085MA14; 1908085MA03), the Key University Science Research Project of Anhui Province (Grant No.KJ2018A0433) and Research Project of Chuzhou University (Grant No.zrjz2017005).
 Author Name Affiliation Shuliang HUANG School of Mathematics and Finance, Chuzhou University, Anhui 239000, P. R. China
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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.