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...

ver descrição completa

Detalhes bibliográficos
Autores: Berni, Jean Cerqueira [UNESP], Mariano, Hugo Luiz
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2024
País:Brasil
Recursos:Universidade Estadual Paulista (UNESP)
Repositório:Repositório Institucional da UNESP
Idioma:inglês
OAI Identifier:oai:repositorio.unesp.br:11449/306408
Acesso em linha:http://dx.doi.org/10.48308/cgasa.21.1.211
https://hdl.handle.net/11449/306408
Access Level:Acceso aberto
Palavra-chave:Boolean algebras
C∞−Rings
Stone duality
Von Neumann Regular Rings
Descrição
Resumo: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.