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

Hashem Bordbar, Young Bae Jun and Seok-Zun Song
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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

Mathematics, 2020, vol. 8, issue 4, 1-10

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 ) .

Keywords: zeromeet element; meet ideal; relative annihilator; semi-prime map; meet map; (semi-prime, meet) weak closure operation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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