Finite direct products of EQ-algebras
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The aim of this paper is to improve the filters of EQ-algebras proposed by V. Novák and B. De Baets. We give a new class of EQ-algebras, namely multiplicatively relative EQ-algebras, and investigate their properties. Particularly, following the work “The lattice of prefilters of an EQ-algebra,” we give a characterization of filter generated by a nonempty subset of multiplicatively relative EQ-algebras. In addition, we give the concrete forms of Spec(E) and Max(E) in an EQ-algebra E, which are finite direct products of special types of EQ-algebras.
KeywordsMultiplicatively relative EQ-algebra Filter Local EQ-algebra Finite direct product
The authors are highly grateful to the editor and anonymous referees for their careful reading and valuable suggestions which helped to improve the paper. This research is supported by a grant of Scientific Research Project of Shaanxi Provincial Department of Education (18JK0407).
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Conflict of Interest
The authors declare that there is no conflict of interests.
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent was obtained from all individual participants included in the study.
- Leuştean L (2004) Representations of many-valued algebras. Ph.D. thesis, University of BucharestGoogle Scholar
- Novák V (2006) EQ-algebras: primary concepts and properties. In: Proceedings of the Czech–Japan seminar, ninth meeting, Kitakyushu and Nagasaki, 18–22 August , Graduate School of Information, Waseda University, pp 219–223Google Scholar
- Yang J, Xin X L, He P F On topological \(EQ\)-algebras, Iranian Journal of Fuzzy Systems, https://doi.org/10.22111/IJFS.2018.3550.