Next Article in Journal
Optimum Design of Infinite Perforated Orthotropic and Isotropic Plates
Next Article in Special Issue
Linear Operators That Preserve Two Genera of a Graph
Previous Article in Journal
Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review
Previous Article in Special Issue
Integral Domains in Which Every Nonzero w-Flat Ideal Is w-Invertible

Open AccessArticle

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

by 2 and
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
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.