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

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.08629
 arXiv:
 arXiv:2404.08629
 Bibcode:
 2024arXiv240408629C
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Category Theory;
 Mathematics  Logic;
 13B30;
 20A05;
 16S99;
 16B50;
 06E99
 EPrint:
 arXiv admin note: substantial text overlap with arXiv:1905.09617