(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this article, we examine the commutativity of a ring Ω endowed with a specific kind of mappings called centrally extended (Φ, m)-homoderivations, where Φ is a mapping on Ω, and m is an integer. This mapping is a comprehensive kind of the homoderivation, Φ- homoderivation, and m -homoderivation. Besides, we provide some properties of its center.