%0 Journal Article
%T Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Berni, Jean Cerqueira
%A Mariano, Hugo Luiz
%D 2024
%\ 07/01/2024
%V 21
%N 1
%P 211-239
%! Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings
%K $\mathcal{C}^{\infty}-$Rings
%K Von Neumann Regular Rings
%K Stone duality
%K Boolean algebras
%R 10.48308/cgasa.2024.104726
%X 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.
%U https://cgasa.sbu.ac.ir/article_104726_3e222ce0a1f73f8d65b576ccf45c1325.pdf