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

Authors

  • Xiaoxue Zhang School of Mathematics and Statistics, Shandong Normal University, 250014, Jinan, P. R. China
  • Hongxing Liu School of Mathematics and Statistics, Shandong Normal University, 250014, Jinan, P. R. China

DOI:

https://doi.org/10.23755/rm.v43i0.786

Keywords:

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

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.

References

Roberto L Cignoli, Itala M d’Ottaviano, and Daniele Mundici. Algebraic foundations of many-valued reasoning. Springer Science & Business Media, 2013.

Anatolij Dvureˇcenskij and Omid Zahiri. On emv-algebras. Fuzzy Sets and Systems, 373:116–148, 2019.

Ronald C Freiwald. An introduction to set theory and topology. Washington University in St. Louis, 2014.

Richard Garner. Ultrafilters, finite coproducts and locally connected classifying toposes. Annals of Pure and Applied Logic, 171(10):102831, 2020.

Celestin Lele, Jean B Nganou, and Christian MS Oumarou. Ideals of semisimple mv-algebras and convergence along set-theoretic filters. Fuzzy Sets and Systems, 2021.

James Munkres. Topology (2nd Edition). Prentice-Hall, Inc, 2000.

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Published

2022-12-30

Issue

Vol. 43 (2022)

Section

Volume 43-2022

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