# Ore extensions for function algebras

## TL;DR

This paper studies Ore extensions of function algebras with finite support, providing explicit formulas for twisted derivations, and describing the algebra's center and centralizer, especially when the derivation is zero.

## Contribution

It offers explicit formulas for twisted derivations and characterizes the center and centralizer of Ore extensions for function algebras, advancing understanding of their algebraic structure.

## Key findings

- Explicit formulas for twisted derivations on the algebra
- Description of the centralizer of the algebra
- Characterization of the center when derivation is zero

## Abstract

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 $\mathcal{A}.$ We give a description for the centralizer of $\mathcal{A},$ and the center of the Ore extension algebra when the derivation is zero.