Connections Between Ideals Of Semisimple Emv-algebras And Set-theoretic Filters

Abstract

In this paper, we mainly study connections between ideals of the semisimple EMV-algebra M and filters on some nonempty set Ω. We show that there is a bijection between the set of all closed ideals of M and the set of all filters on Ω. We prove that the topological space of all closed prime ideals of M and the topological space of all weak ultrafilters on Ω are homeomorphic.

Keywords

• semisimple emv-algebra
• ideal
• filter
• closure operation
• closed ideal