Commutative True-False ideals in BCI/BCK-algebras

نویسندگان
Borzooei, Rajab Ali ID 1
Mohseni Takallo, Mohammad ID 2
Aaly Kologani, Mona ID 3
Jun, Young Bae ID 4

1 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

3 Hatef Higher Education Institute, Zahedan, Iran.

4 Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea.

doi
10.22034/as.2023.3027
چکیده

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 $T\&F$-ideal 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. 

کلیدواژه‌ها
Closed $T\&F$-ideal, (limited) Commutative $T\&F$-ideal, (limited) $T\&F$-ideal, (limited) $T\&F$-subalgebra, $T\&F$-$\circ$-subalgebra, True-False structure