Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 2 2024 03 01 Commutativity of prime ring with generalized skew derivations having a Lie-type behaviour 95 111 196583 10.30504/jims.2024.443925.1161 EN G. Scudo Department of Engineering, University of Messina, Messina, Italy. 0000-0002-4478-5589 Journal Article 2024 02 14 Let $R$ be a prime ring of characteristic different from‎ ‎$2$ and $3$‎, ‎$Q_r$ its right Martindale quotient ring and‎ ‎$C$ its the extended centroid‎. ‎Suppose that $F$ is a non-zero generalized skew derivation of $R$ such that‎ ‎$F([x,y]_k)=[F(x),y]_k+[x,F(y)]_k$‎ ‎for all $x,y\in R$‎, ‎with $k>1$ fixed integer‎. ‎In this paper we will showw that‎, ‎then $R$ is commutative‎. $$F([x; y]_k) = [F(x); y]_k + [x; F(y)]_k$$ for all $x, y \in R$, with $k > 1$ fixed integer. Then $R$ is commutative. Generalized skew derivations Prime rings Lie derivations https://jims.ims.ir/article_196583_4d7d7c7b39ef4713553ea7935fa4605d.pdf