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arXiv · 2211.06589

On commutativity of prime rings with skew derivations

Nadeem ur Rehman·Shuliang Huang
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Abstract

Let $\mathscr{R}$ be a prime ring of Char$(\mathscr{R}) \neq 2$ and $m\neq 1$ be a positive integer. If $S$ is a nonzero skew derivation with an associated automorphism $\mathscr{T}$ of $\mathscr{R}$ such that $([S([a, b]), [a, b]])^{m} = [S([a, b]), [a, b]]$ for all $a, b \in \mathscr{R}$, then $\mathscr{R}$ is commutative.

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Nadeem ur Rehman, Shuliang Huang. 2022-11-21. On commutativity of prime rings with skew derivations. https://doi.org/10.46298/cm.10319

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