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

Xiaoxue Zhang, Hongxing Liu


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.


Semisimple EMV-algebra; Ideal; Filter; Closure operation; Closed ideal

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.