Classification of Boolean algebras through von Neumann regular \mathcal{C}^{\infty}-rings

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.

کلیدواژه ها:

\mathcal{C}^{\infty}-Rings ، Von Neumann Regular Rings ، Stone duality ، Boolean algebras