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

Xiaoxue Zhang, Hongxing Liu

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

Full Text:

PDF

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.




DOI: http://dx.doi.org/10.23755/rm.v43i0.786

Refbacks

  • There are currently no refbacks.


Copyright (c) 2022 Xiaoxue Zhang, Hongxing Liu

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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