Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585321120240701Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings21123910472610.48308/cgasa.2024.104726ENJean CerqueiraBerniDepartment of Mathematics
IGCE - São Paulo State UniversityHugo LuizMarianoDepartment of Mathematics, Institute of Mathematics and Statistics, University of São Paulo0000-0002-9745-2411Journal Article20240804In 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.https://cgasa.sbu.ac.ir/article_104726_3e222ce0a1f73f8d65b576ccf45c1325.pdf