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AIMS Mathematics

2021, Volume 6, Issue 8: 8567-8584. doi: 10.3934/math.2021497
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Commutative ideals of BCK-algebras and BCI-algebras based on soju structures

  • 1.
    Department of Mathematics, Jeju National University, Jeju 63243, Korea
  • 2.
    Research Institute for Natural Science, Department of Mathematics, Hanyang University, Seoul 04763, Korea
  • 3.
    Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
  • Received: 23 March 2021 Accepted: 26 May 2021 Published: 07 June 2021

  • MSC : 03G25, 06F35, 06D72

  • 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.

    Citation: Seok-Zun Song, Hee Sik Kim, Young Bae Jun. Commutative ideals of BCK-algebras and BCI-algebras based on soju structures[J]. AIMS Mathematics, 2021, 6(8): 8567-8584. doi: 10.3934/math.2021497

    Related Papers:

  • 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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