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Abstract
The notion of a belligerent GE-filter in a GE-algebra is introduced, and the relationships between a GE-filter and a belligerent GE-filter will be given. Conditions for a GE-filter to be a belligerent GE-filter are provided. The product and the union of GE-algebras are discussed and its properties are investigated.
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References
- Bandaru, R., Saeid, A. B., and Jun, Y. B., “On GE-algebras”, Bull. Sect. Log., 50:1 (2021), 81–96. https://doi.org/10.18778/0138-0680.2020.20
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- Chajda, I., Halas, R. and Jun, Y. B., “Annihilators and deductive systems in commutative Hilbert algebras”, Comment. Math. Univ. Carolinae, 43:3 (2002), 407–417.
- Diego, A., Sur les algebres de Hilbert, Collection de Logique Mathematique, Edition Hermann, Serie A, XXI, 1966.
- Jun, Y. B., “Commutative Hilbert algebras”, Soochow J. Math., 22:4 (1996), 477–484.
- Jun, Y. B. and Kim, K. H., H-filters of Hilbert algebras, Sci. Math. Jpn., e-2005, 231- 236.
- Najafi, A. and Borumand Saeid, A., “Fuzzy points in BE-algebras”, J. Mahani Math. Research Center, 8:1-2 (2019). 69-80. DOI: 10.22103/jmmrc.2019.12457.1065
- Nasab, A. S. and Borumand Saeid, A., “Semi maximal filter in Hilbert algebras”, J. Intell. Fuzzy Syst., 30 (2016), 7–15. DOI:10.3233/IFS-151706
- Nasab, A. S. and Borumand Saeid, A., “Stonean Hilbert algebra”, J. Intell. Fuzzy Syst., 30 (2016), 485–492. DOI:10.3233/IFS-151773
- Nasab, A. S. and Borumand Saeid, A., “Study of Hilbert algebras in point of filters”, An St. Univ. Ovidius Constanta, 24:2 (2016), 221–251. DOI: 10.1515/auom-2016-003
References
Bandaru, R., Saeid, A. B., and Jun, Y. B., “On GE-algebras”, Bull. Sect. Log., 50:1 (2021), 81–96. https://doi.org/10.18778/0138-0680.2020.20
Borzooei, R. A. and Shohani, J., “On generalized Hilbert algebras”, Ital. J. Pure Appl. Math., 29 (2012), 71–86.
Chajda, I. and Halas, R., “Congruences and idealas in Hilbert algebras”, Kyungpook Math. J., 39 (1999), 429–432.
Chajda, I., Halas, R. and Jun, Y. B., “Annihilators and deductive systems in commutative Hilbert algebras”, Comment. Math. Univ. Carolinae, 43:3 (2002), 407–417.
Diego, A., Sur les algebres de Hilbert, Collection de Logique Mathematique, Edition Hermann, Serie A, XXI, 1966.
Jun, Y. B., “Commutative Hilbert algebras”, Soochow J. Math., 22:4 (1996), 477–484.
Jun, Y. B. and Kim, K. H., H-filters of Hilbert algebras, Sci. Math. Jpn., e-2005, 231- 236.
Najafi, A. and Borumand Saeid, A., “Fuzzy points in BE-algebras”, J. Mahani Math. Research Center, 8:1-2 (2019). 69-80. DOI: 10.22103/jmmrc.2019.12457.1065
Nasab, A. S. and Borumand Saeid, A., “Semi maximal filter in Hilbert algebras”, J. Intell. Fuzzy Syst., 30 (2016), 7–15. DOI:10.3233/IFS-151706
Nasab, A. S. and Borumand Saeid, A., “Stonean Hilbert algebra”, J. Intell. Fuzzy Syst., 30 (2016), 485–492. DOI:10.3233/IFS-151773
Nasab, A. S. and Borumand Saeid, A., “Study of Hilbert algebras in point of filters”, An St. Univ. Ovidius Constanta, 24:2 (2016), 221–251. DOI: 10.1515/auom-2016-003