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arXiv · 2404.08629

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

Jean Cerqueira Berni·Hugo Luiz Mariano
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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.

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Jean Cerqueira Berni, Hugo Luiz Mariano. 2024-04-12. Classification of Boolean Algebras through von Neumann regular $\mathcal{C}^{\infty}-$Rings. https://arxiv.org/abs/2404.08629

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