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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.
Berni et al. (Fri,) studied this question.
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