A Study of Central Identities Equipped with Skew Lie Product Involving Generalized Derivations

Let R be a ring with involution \(\sigma \) . Notation \( \nabla [t_1,t_2]\) denotes the skew Lie product and defined by \(t_1 t_2-t_2 \sigma (t_1)\) . The main objective of this paper is to investigate the commutativity of \(\sigma \) -prime rings with involution \(\sigma \) of the second kind equipped with skew Lie product involving generalized derivation. Finally, we provide some examples to demonstrate that the conditions assumed in our results are necessary.