Looking at Two Ways of Constructing Quotient Hyper $BN$-algebras and Some Notes on Hyper $BN$-ideals

Authors

  • Lyster Rey Cabardo Mindanao State University - Iligan Institute of Technology
  • Gaudencio Petalcorin Jr. Mindanao State University - Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.5003

Keywords:

hyper $BN$-algebras, hyper $BN$-ideals, quotient hyper $BN$-algebras

Abstract

A hyper $BN$-algebra is a nonempty set $H$ together with a hyperoperation ``$\circledast$'' and a constant $0$ such that for all $x, y, z \in H$: $x \ll x$, $x \circledast 0 = \{x\}$, and $(x \circledast y) \circledast z = (0 \circledast z) \circledast (y \circledast x)$, where $x \ll y$ if and only if $0 \in x \circledast y$. We investigated the structures of ideals in the Hyper $BN$-algebra setting. We established equivalency of weak hyper $BN$-ideals and hyper sub$BN$-algebras. Also, we found a condition when a strong hyper $BN$-ideal become a hyper $BN$-ideal. Finally, we looked at two ways in constructing the quotient hyper $BN$-algebras and investigated the relationship between the two constructions.

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Published

2024-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Looking at Two Ways of Constructing Quotient Hyper $BN$-algebras and Some Notes on Hyper $BN$-ideals. (2024). European Journal of Pure and Applied Mathematics, 17(1), 222-242. https://doi.org/10.29020/nybg.ejpam.v17i1.5003