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JNB-ALGEBRASopen access
- Issue Date
- Nov-2025
- Publisher
- Shahrood University of Technology
- Keywords
- JNB-Algebra; JNB-Deductive system; JNB-Filter; JNB-Subalgebra; Upper set
- Citation
- Journal of Algebraic Systems, v.13, no.3, pp 45 - 62
- Pages
- 18
- Indexed
- SCOPUS
ESCI
- Journal Title
- Journal of Algebraic Systems
- Volume
- 13
- Number
- 3
- Start Page
- 45
- End Page
- 62
- ISSN
- 2345-511X
2345-511X
- 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. © 2025, Shahrood University of Technology. All rights reserved.
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