# Local Derivations of Finitary Incidence Algebras

## TL;DR

This paper proves that every R-linear local derivation of finitary incidence algebras over a poset is actually a derivation, extending previous results in the algebraic structure of these algebras.

## Contribution

It generalizes a known result by showing that local derivations are derivations in the context of finitary incidence algebras over a poset.

## Key findings

- Every R-linear local derivation of FI(P,R) is a derivation
- Generalizes previous results by Nowicki and Nowosad
- Extends understanding of derivation structures in incidence algebras

## Abstract

Let $P$ be a partially ordered set, $R$ a commutative ring with identity and $FI(P,R)$ the finitary incidence algebra of $P$ over $R$. In this note we prove that each $R$-linear local derivation of $FI(P,R)$ is a derivation, which partially generalizes a result by Nowicki and Nowosad.