Commutative True-False ideals in BCI/BCK-algebras

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.

کلیدواژه ها:

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