Nadeem ur Rehman ; Shuliang Huang - On commutativity of prime rings with skew derivations

cm:10319 - Communications in Mathematics, November 22, 2022, Volume 31 (2023), Issue 1 - https://doi.org/10.46298/cm.10319
On commutativity of prime rings with skew derivations

Authors: Nadeem ur Rehman ; Shuliang Huang

    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.


    Volume: Volume 31 (2023), Issue 1
    Published on: November 22, 2022
    Accepted on: November 17, 2022
    Submitted on: November 17, 2022
    Keywords: Mathematics - Rings and Algebras,16W25, 16N60

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