2021•AIMS MathematicsOpen access

Commutative ideals of BCK-algebras and BCI-algebras based on soju structures

Seok-Zun Song, Hee Sik Kim, Young Bae Jun

Abstract

The concept of a commutative soju ideal in a BCK-algebra and a BCI-algebra is introduced, and their properties are investigated. The relationship between a soju ideal and a commutative soju ideal are discussed, and examples to show that any soju ideal may not be a commutative soju ideal are provided. Conditions for a soju ideal to be a commutative soju ideal are considered, and characterizations of a commutative soju ideal are studied. A new commutative soju ideal using the given commutative soju ideal is maded, and the extension property for a commutative soju ideal is established. A commutative soju ideal is established by using a commutative ideal of a BCI-algebra. The notion of a closed soju ideal in a BCI-algebra is also introduced, and it is used in studying the characterization of a commutative soju ideal.

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Key concepts: Primary ideal, Ideal theory, Ideal (ethics), Radical of an ideal, Commutative property, Mathematics, Minimal ideal, Maximal ideal