Classification of Boolean Algebras through von Neumann regular $\mathcal{C}^{\infty}-$Rings

Published 12 Apr 2024 in math.RA, math.CT, and math.LO | (2404.08629v1)

Abstract: In this paper, we introduce the concept of a "von Neumann regular $\mathcal{C}^{{\infty}$-ring",} which is a model for a specific equational theory. We delve into the characteristics of these rings and demonstrate that each Boolean space can be effectively represented as the image of a von Neumann regular $\mathcal{C}^{{\infty}$-ring} through a specific functor. Additionally, we establish that every homomorphism between Boolean algebras can be expressed through a $\mathcal{C}^{{\infty}$-ring} homomorphism between von Neumann regular $\mathcal{C}^{{\infty}$-rings.}