classification of boolean algebras through von neumann regular c∞−rings

In this paper, we introduce the concept of a “von neumann regular c ∞-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 c ∞-ring through a specific functor. additionally, we establish that every homomorphism between boolean algebras can be expressed through a c ∞- ring homomorphism between von neumann regular c ∞-rings.