JNB-ALGEBRAS

Document Type : Original Manuscript

Authors

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

2 Department of Mathematics, Bapatla Engineering College, P.O. Box 522 101, Bapatla, Andhra Pradesh, India.

3 Department of Mathematics, School of Advanced Sciences, VIT-AP University, P.O. Box 522237, Andhra Pradesh, India.

Abstract

As a generalization of the self-distributive BE-algebra, the JNB-algebra is introduced, and its basic properties are investigated. This could play various roles in the study of logical algebra, including BCK-algebra. First, examples are presented showing that the three axioms of JNB-algebra are independent of each other. The basic properties of JNB-algebras that will be needed to study various theories about JNB-algebras are explored. Upper sets based on one and two elements are introduced and its associated properties are examined. Two concepts so called JNB-deductive system and JNB-filter are introduced, and their properties are investigated. Characterizations of the JNB-deductive system and the JNB-filter are discussed. It is finally confirmed that the JNB-deductive system matches the JNB-filter.

Keywords

References

 1. J. C. Abbott, Semi-Boolean algebra, Mat. Vesnik, 4(19) (1967), 177–198.
 
2. S. S. Ahn and K. S. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn., 68(2) (2008), 279–285.
 
3. R. K. Bandaru, A. Borumand Saeid and Y. B. Jun, On GE-algebras, Bull. Sect. Logic Univ. Łódź, 50(1) (2021), 81–96.
 
4. A. Borumand Saeid, A. Rezaei and R. A. Borzooei, Some types of filters in BE-algebras, Math. Comput. Sci., 7 (2013), 341–352.
 
5. R. A. Borzooei and S. K. Shoar, Implication algebras are equivalent to the dual implicative BCK-algebras, Sci. Math. Jpn., 63(3) (2006), 429–432.
 
6. R. A. Borzooei and J. Shohani, On generalized Hilbert algebras, Ital. J. Pure Appl. Math., 29 (2012), 71–86.
 
7. I. Chajda and R. Halas, Congruences and ideals in Hilbert algebras, Kyungpook Math. J., 39 (1999), 429–432.
 
8. I. Chajda, R. Halas and Y. B. Jun, Annihilators and deductive systems in commutative Hilbert algebras, Comment. Math. Univ. Carolin., 43(3) (2002), 407–417.
 
9. A. Diego, Sur les algebres de Hilbert, Collection de Logique Mathematique, Edition Hermann, Serie A, XXI, 1966.
 
10. Y. B. Jun, Commutative Hilbert algebras, Soochow J. Math., 22(4) (1996), 477–484.
 
11. H. S. Kim and Y. H. Kim, On BE-algebras, Sci. Math. Jpn., 66(1) (2007), 113–116.
 
12. A. Rezaei, A. Borumand Saeid and R. A. Borzooei, Relation between Hilbert algebras and BE-algebras, Appl. Appl. Math., 8 (2013), 573–584 
Journal of Algebraic Systems
Volume 13, Issue 3
November 2025
Pages 45-62

Files

Share

How to cite

Statistics