Classification of Boolean algebras through von Neumann regular C∞−rings
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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.
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Boolean algebras, C∞−Rings, Stone duality, Von Neumann Regular Rings
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Inglês
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Categories and General Algebraic Structures with Applications, v. 21, n. 1, p. 211-239, 2024.
