TY - JOUR
ID - 104726
TI - Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Berni, Jean Cerqueira
AU - Mariano, Hugo Luiz
AD - Department of Mathematics
IGCE - São Paulo State University
AD - Department of Mathematics, Institute of Mathematics and Statistics, University of São Paulo
Y1 - 2024
PY - 2024
VL - 21
IS - 1
SP - 211
EP - 239
KW - $\mathcal{C}^{\infty}-$Rings
KW - Von Neumann Regular Rings
KW - Stone duality
KW - Boolean algebras
DO - 10.48308/cgasa.2024.104726
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_104726.html
L1 - https://cgasa.sbu.ac.ir/article_104726_3e222ce0a1f73f8d65b576ccf45c1325.pdf
ER -