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

Document Type : Research Paper

Authors

1 Department of Mathematics IGCE - São Paulo State University

2 Department of Mathematics, Institute of Mathematics and Statistics, University of São Paulo

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.

Keywords


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