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Mathematics > Rings and Algebras
Title: Classification of Boolean Algebras through von Neumann regular $\mathcal{C}^{\infty}-$Rings
(Submitted on 12 Apr 2024)
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.
Submission history
From: Jean Cerqueira Berni [view email][v1] Fri, 12 Apr 2024 17:47:18 GMT (46kb)
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