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- Title
EXTENDED BCK-IDEAL BASED ON SINGLE-VALUED NEUTROSOPHIC HYPER BCK-IDEALS.
- Authors
Hamidi, Mohammad
- Abstract
This paper introduces the concept of single-valued neutrosophic hyper BCKsubalgebras 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 BCKsubalgebra) BCK-(sub)algebra.
- Subjects
CONGRUENCE lattices; RELATION algebras; ALGEBRA; GENERALIZATION
- Publication
Bulletin of the Section of Logic, 2023, Vol 52, Issue 4, p411
- ISSN
0138-0680
- Publication type
Article
- DOI
10.18778/0138-0680.2023.20