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Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras

Author

Listed:
  • Hashem Bordbar

    (Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Vipavska 13, Slovenia)

  • Young Bae Jun

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea)

  • Seok-Zun Song

    (Department of Mathematics, Jeju National University, Jeju 690-756, Korea)

Abstract

We introduce the notions of meet, semi-prime, and prime weak closure operations. Using homomorphism of BCK-algebras φ : X → Y , we show that every epimorphic image of a non-zeromeet element is also non-zeromeet and, for mapping c l Y : I ( Y ) → I ( Y ) , we define a map c l Y ← on I ( X ) by A ↦ φ − 1 ( φ ( A ) c l Y ) . We prove that, if “ c l Y ” is a weak closure operation (respectively, semi-prime and meet) on I ( Y ) , then so is “ c l Y ← ” on I ( X ) . In addition, for mapping c l X : I ( X ) → I ( X ) , we define a map c l X → on I ( Y ) as follows: B ↦ φ ( φ − 1 ( B ) c l X ) . We show that, if “ c l X ” is a weak closure operation (respectively, semi-prime and meet) on I ( X ) , then so is “ c l X → ” on I ( Y ) .

Suggested Citation

  • Hashem Bordbar & Young Bae Jun & Seok-Zun Song, 2020. "Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:567-:d:344460
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