Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings
نویسندگان
1 Department of Mathematics, S˜ao Paulo State University - UNESP, 13506-900 , S˜ao Paulo, Brazil.
2 o Department of Mathematics, University of S˜ao Paulo, 05508-090, S˜ao Paulo, Brazil.
doi
10.48308/cgasa.2024.104726چکیده
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.
