Commuting maps of inflated algebras

Commuting maps on a class of algebras called inflated algebras are investigated. In particular, we can prove that every commuting map $\theta$ on such an algebra is of the form $\theta(x)=c x+\mu(x)$, where $c$ belongs to the base field $K$ of characteristic not 2, and $\mu$ is a central-valued linear map.