  In this paper we present the notion of a von Neumann regular
$\mathcal{C}^{\infty}-$ring, we prove some results about them and we describe
some of their properties. We prove, using two different methods, that the
category of von Neumann regular $\mathcal{C}^{\infty}-$rings is a reflective
subcategory of $\mathcal{C}^{\infty}{\rm \bf Rng}$. We prove that every
homomorphism between Boolean algebras can be represented by a
$\mathcal{C}^{\infty}-$ring homomorphism between von Neumann regular
$\mathcal{C}^{\infty}-$rings.
