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Finite direct products of EQ-algebras

  • Jiang YangEmail author
  • Xiongwei Zhang
Foundations
  • 26 Downloads

Abstract

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.

Keywords

Multiplicatively relative EQ-algebra Filter Local EQ-algebra Finite direct product 

Notes

Acknowledgements

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).

Compliance with ethical standards

Conflict of Interest

The authors declare that there is no conflict of interests.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Arts and SciencesShaanxi University of Science and TechnologyXi’anChina
  2. 2.School of Mathematics and StatisticsYulin UniversityYulinChina

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