Document Type : Original Manuscript


1 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, P.O. Box 76169-14111, Kerman, Iran.

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

3 Department of Mathematics, GITAM(Deemed to be University), P.O. Box 502329 Telangana State, India.

4 Department of Mathematics Education, Gyeongsang National University, P.O. Box 52828, Jinju, Korea.


Further properties on (belligerent) GE-filters are discussed, and the quotient GEalgebra via a GE-filter is established. Conditions for the set →
c to be a belligerent GE-filter
are provided. The extension property of belligerent GE-filter is composed. The notions of a
balanced element, a balanced GE-filter, an antisymmetric GE-algebra and a voluntary GE-filter
are introduced, and its properties are examined. The relationship between a GE-subalgebra
and a GE-filter is established. Conditions for every element in a GE-algebra to be a balanced
element are provided. The conditions necessary for a GE-filter to be a voluntary GE-filter are
considered. The GE-filter generated by a given subset is established, and its shape is identified


1. R. K. Bandaru, A. B. Saeid and Y. B. Jun, Belligerent GE-filter in GE-algebras, Thai J. Math. (submitted).
2. R. K. Bandaru, A. B. Saeid and Y. B. Jun, On GE-algebras, Bull. Sect. Log., 50(1) (2021), 81–96.
3. R. A. Borzooei and J. Shohani, On generalized Hilbert algebras, Ital. J. Pure Appl. Math., 29 (2012), 71–86.
4. I. Chajda and R. Halas, Congruences and idealas in Hilbert algebras, Kyungpook Math. J., 39 (1999), 429–432.
5. I. Chajda, R. Halas and Y. B. Jun, Annihilators and deductive systems in commutative Hilbert algebras, Comment. Math. Univ. Carolin., 43(3) (2002), 407–
6. A. Diego, Sur les algebres de Hilbert, Collection de Logique Mathematique, Edition Hermann, Serie A, XXI, 1966.
7. Y. B. Jun, Commutative Hilbert algebras, Soochow J. Math., 22(4) (1996), 477– 484.
8. Y. B. Jun and K. H. Kim, H-filters of Hilbert algebras, Sci. Math. Jpn., e-2005,
9. H. S. Kim and Y. H. Kim, On BE-algebras, Sci. Math. Jpn., 66 (2007), 113–116.
10. A. S. Nasab and A. B. Saeid, Semi maximal filter in Hilbert algebra, J. Intell. Fuzzy Syst., 30 (2016a), 7–15.
11. A. S. Nasab and A. B. Saeid, Stonean Hilbert algebra, J. Intell. Fuzzy Syst., 30 (2016b), 485–492.
12. A. S. Nasab and A. B. Saeid, Study of Hilbert algebras in point of filters, An. Stiint. Univ. Ovidius Constanta Ser. Mat., 24(2) (2016), 221–251.