Extended BCK-Ideal Based on Single-Valued Neutrosophic Hyper BCK-Ideals

Mohammad Hamidi

doi:10.18778/0138-0680.2023.20

Authors

Mohammad Hamidi University of Payame Noor, Department of Mathematics https://orcid.org/0000-0002-8686-6942

DOI:

https://doi.org/10.18778/0138-0680.2023.20

Keywords:

single-valued neutrosophic (hyper)\(BCK\)-subalgebra, quasi commutative diagram, extendable single-valued neutrosophic (hyper)\(BCK\)-ideal

Abstract

This paper introduces the concept of single-valued neutrosophic hyper \(BCK\)-subalgebras as a generalization and alternative of hyper \(BCK\)-algebras and on any given nonempty set constructs at least one single-valued neutrosophic hyper \(BCK\)-subalgebra and one a single-valued neutrosophic hyper \(BCK\)-ideal. In this study level subsets play the main role in the connection between singlevalued neutrosophic hyper \(BCK\)-subalgebras and hyper \(BCK\)-subalgebras and the connection between single-valued neutrosophic hyper \(BCK\)-ideals and hyper \(BCK\)-ideals. The congruence and (strongly) regular equivalence relations are the important tools for connecting hyperstructures and structures, so the major contribution of this study is to apply and introduce a (strongly) regular relation on hyper \(BCK\)-algebras and to investigate their categorical properties (quasi commutative diagram) via single-valued neutrosophic hyper \(BCK\)-ideals. Indeed, by using the single-valued neutrosophic hyper \(BCK\)-ideals, we define a congruence relation on (weak commutative) hyper \(BCK\)-algebras that under some conditions is strongly regular and the quotient of any (single-valued neutrosophic)hyper \(BCK\)-(sub)algebra via this relation is a (single-valued neutrosophic)(hyper \(BCK\)-subalgebra) \(BCK\)-(sub)algebra.

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