Ore extensions for function algebras

In this article we consider the Ore extension Algebra for the algebra $\mathcal{A}$ of functions with finite support on a countable set. We derive explicit formulas for twisted derivations on $\mathcal{A}\mathrm{.}$ We give a description for the centralizer of $\mathcal{A},$ and the center of the Ore extension algebra when the derivation is zero.