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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 63, Issue 5


Fuzzy filters of BE-algebras

Grzegorz Dymek
  • Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, PL-20-708, Lublin, Poland
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/ Andrzej Walendziak
  • Institute of Mathematics and Physics, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, PL-08-110, Siedlce, Poland
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Published Online: 2013-11-01 | DOI: https://doi.org/10.2478/s12175-013-0145-y


Characterizations of fuzzy filters in a BE-algebra are established. Conditions for a fuzzy set to be a fuzzy filter are given. For a fuzzy set µ the least fuzzy filter containing µ is constructed. The homomorphic properties of fuzzy filters of a BE-algebra are provided. Finally, characterizations of Noetherian BE-algebras and Artinian BE-algebras via fuzzy filters are obtained.

MSC: Primary 03G25; Secondary 06F35

Keywords: BE-algebra; fuzzy filter; Noetherian (Artinian) BE-algebra

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About the article

Published Online: 2013-11-01

Published in Print: 2013-10-01

Citation Information: Mathematica Slovaca, Volume 63, Issue 5, Pages 935–946, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-013-0145-y.

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© 2013 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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