Von Neumann Regular $\mathcal{C}^{\infty}-$Rings and Applications

Published 23 May 2019 in math.CT | (1905.09617v1)

Abstract: 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.}