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

Author:

Bordbar HashemORCID,Jun Young Bae,Song Seok-ZunORCID

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 ) .

Funder

National Research Foundation of Korea

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference13 articles.

1. Weak closure operations on ideals of BCK-algebras;Bordbar;J. Comput. Anal. Appl.,2017

2. Tender and naive weak closure operations on lower BCK-semilattices;Bordbar;J. Comput. Anal. Appl.,2017

3. A Finite Type of Closure Operations on BCK-algebras

4. SEMI-PRIME CLOSURE OPERATIONS ON BCK-ALGEBRA

5. Semi-prime and meet weak closure operations in lower BCK-semilattices;Bordbar;Quasigruops Relat. Syst.,2017

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