Fuzzy filters of BE-algebras |
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| Authors: | Grzegorz Dymek Andrzej Walendziak |
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| Affiliation: | 1. Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, PL-20-708, Lublin, Poland
2. Institute of Mathematics and Physics, Siedlce University of Natural Sciences and Humanities, 3 Maja 54, PL-08-110, Siedlce, Poland
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| Abstract: | 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. |
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