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True-False ideals of BCK/BCI-algebras
- Issue Date
- Jan-2024
- Publisher
- TARU Publications
- Keywords
- (limited) T & F-ideal; (limited) T & F-subalgebra; Condition (S); Ideal; Subalgebra; T & F-°-subalgebra; °-subalgebra
- Citation
- Journal of Discrete Mathematical Sciences and Cryptography, v.27, no.1, pp 45 - 62
- Pages
- 18
- Indexed
- SCOPUS
ESCI
- Journal Title
- Journal of Discrete Mathematical Sciences and Cryptography
- Volume
- 27
- Number
- 1
- Start Page
- 45
- End Page
- 62
- ISSN
- 0972-0529
2169-0065
- Abstract
- The notions of a (limited) T & F-ideal and a T & F-°-subalgebra are introduced, and various properties are investigated. The relationship between a T & F-subalgebra and a T & F-ideal is established. Conditions for a T & F-structure (resp., T & F-subalgebra) to be a T & F-ideal are discussed. An example is provided to confirm that in a BCI-algebra, a T & F-ideal cannot be a T & F-subalgebra in general, and then conditions for a T & F-ideal to be a T & F-subalgebra in a BCI-algebra are considered. The relationship between a T & F-ideal and a T & F-°-subalgebra in a BCK-algebra with condition (S) is discussed. Conditions for a T & F-structure over a BCK-algebra with condition (S) to be a T & F-ideal are provided. Using the notion of T & F-level sets, a characterization of a T & F-ideal is established. A novel T & F-ideal is constructed with an existing T & F-ideal using a characterization of a T & F-ideal. © Taru Publications.
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