In this article, we explored the commutativity of a ring $\mathrm{\Lambda }$ that is equipped with a unique class of mappings called centrally extended $n$-homoderivations, where $n$ is an integer. These mappings generalize the concepts of derivations and homoderivations. Furthermore, we investigated specific properties of the center of such rings.

This paper aims to establish the following: Let $\mathrm{\Omega }$ be a ring that satisfies some conditions and has an idempotent element $f\ne 0,1$. We intend to show that if $G$ is any suitable multiplicative generalized CE-derivation of $\mathrm{\Omega }$, then $G$ is a centrally extended additive.