Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 587-603, 2020

Annihilators of skew derivations with Engel conditions on prime rings

Taylan Pehlivan, Emine Albas

Received September 21, 2018. Published online December 16, 2019.

Abstract: 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 $a=0$.

Keywords: prime ring; derivation; skew derivation; automorphism

Classification MSC: 16W20, 16W25

DOI: 10.21136/CMJ.2019.0412-18

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Taylan Pehlivan, Emine Albas, Department of Mathematics, Ege University, C Blok, 35100 Bornova, Izmir, Turkey, e-mail: taylan_pehlivan@hotmail.com, emine.albas@ege.edu.tr

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