(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this article, we will investigate the commutativity of the factor ring /P, where P is a prime ideal of any ring . This investigation will be carried out using generalized P-derivations and associated with P-derivations χ and , respectively, that satisfy specific functional identities linking to P. Moreover, we will discuss some related results. Finally, to reinforce the importance of our assumption regarding the primeness of P, we will provide some examples.