True-False ideals of BCK/BCI-algebras

被引：0
|
作者：
Takallo, M. Mohseni [1 ]
Borzooei, R. A. [1 ]
Rezaei, G. R. [2 ]
Jun, Y. B. [3 ]
机构：
[1] Shahid Beheshti Univ, Dept Math, Tehran, Iran
[2] Univ Sistan & Baluchestan, Dept Math, Zahedan, Iran
[3] Gyeongsang Natl Univ, Dept Math Educ, Jinju 52828, South Korea
来源：
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY | 2024年 / 27卷 / 01期
关键词：
Subalgebra; circle; -subalgebra; Ideal; Condition (S); (limited) T & F-subalgebra; (limited) T & F-ideal; T & F- circle -subalgebra;
D O I：
10.47974/JDMSC-1544
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The notions of a (limited) T & F-ideal and a T & F-circle -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-circle -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.
引用
收藏
页码：45 / 62
页数：18
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