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Open AccessArticle

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

1
Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Vipavska 13, Slovenia
2
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
3
Department of Mathematics, Jeju National University, Jeju 690-756, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 567; https://doi.org/10.3390/math8040567
Received: 25 February 2020 / Revised: 2 April 2020 / Accepted: 2 April 2020 / Published: 11 April 2020
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2020)
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 ) . View Full-Text
Keywords: zeromeet element; meet ideal; relative annihilator; semi-prime map; meet map; (semi-prime, meet) weak closure operation zeromeet element; meet ideal; relative annihilator; semi-prime map; meet map; (semi-prime, meet) weak closure operation
MDPI and ACS Style

Bordbar, H.; Jun, Y.B.; Song, S.-Z. Homomorphic Image and Inverse Image of Weak Closure Operations on Ideals of BCK-Algebras. Mathematics 2020, 8, 567.

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