| Annihilator Condition on Power Values of Commutators with Derivations |
| Received:April 24, 2018 Revised:August 29, 2018 |
| Key Words:
prime ring derivation extended centroid
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| Fund Project: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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2019.05.005 |
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