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Introduces Hom-BCI and Hom-BCK algebras with applications in poset structures and commutativity.
The concept of Hom-BCI-algebras and (commutative) Hom-BCK-algebras is introduced, and examples are provided to illustrate it. Fundamental properties of them are investigated, and a method for deriving the Hom-BCI-algebra and Hom-BCK-algebra from the standard BCI-algebra and BCK-algebra is presented, and vice versa. The poset structure is obtained from the Hom-BCI-algebra, and a characterization of Hom-BCK-algebra is addressed. The semilattice is induced based on the commutative Hom-BCK-algebra. The notion of Hom-initial section is established, and its properties are investigated. It is also used in relation to the commutativity of Hom-BCK-algebra.
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Jun et al. (2026) studied this question.
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