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COMMUTATIVE TRUE-FALSE IDEALS IN BCI/BCK-ALGEBRAS
- Issue Date
- Aug-2023
- Publisher
- Yazd University
- Keywords
- (limited) Commutative T&F-ideal; (limited) T&F-ideal; (limited) T&F-subalgebra; Closed T&F-ideal; T&F-◦-subalgebra; True-False structure
- Citation
- Algebraic Structures and their Applications, v.10, no.2, pp 155 - 172
- Pages
- 18
- Indexed
- SCOPUS
- Journal Title
- Algebraic Structures and their Applications
- Volume
- 10
- Number
- 2
- Start Page
- 155
- End Page
- 172
- ISSN
- 2423-3447
2423-3447
- Abstract
- The notion of a (limited) commutative T&F-ideal in BCK-algebras and BCI-algebras is introduced, and their properties are investigated. A relationship between a T&Fideal and a commutative T&F-ideal in BCK-algebras and BCI-algebras is established, and examples to show that any T&F-ideal may not be commutative are given. Proper conditions for a T&F-ideal to be commutative are provided. Using a commutative ideal of a BCK-algebra and a BCI-algebra, a commutative T&F-ideal is established. The closed T&F-ideal in a BCI-algebra is introduced, and a condition for a closed T&F-ideal to be commutative is discussed. Characterization of a commutative T&F-ideal in a BCI-algebra is considered. © 2023 Yazd University.
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