# Jordan Isomorphisms of Finitary Incidence Algebras

## TL;DR

This paper characterizes Jordan isomorphisms of finitary incidence algebras over certain rings, showing they decompose into sums of homomorphisms and anti-homomorphisms, advancing understanding of algebraic structure mappings.

## Contribution

It proves that every R-linear Jordan isomorphism of finitary incidence algebras can be expressed as a near-sum of a homomorphism and an anti-homomorphism, revealing their structural decomposition.

## Key findings

- Jordan isomorphisms decompose into near-sums of homomorphisms and anti-homomorphisms
- The result applies to finitary incidence algebras over 2-torsionfree rings
- Provides a structural characterization of algebra isomorphisms in this context

## Abstract

Let $X$ be a partially ordered set, $R$ a commutative $2$-torsionfree unital ring and $FI(X,R)$ the finitary incidence algebra of $X$ over $R$. In this note we prove that each $R$-linear Jordan isomorphism of $FI(X,R)$ onto an $R$-algebra $A$ is the near-sum of a homomorphism and an anti-homomorphism.