(untitled) (European Journal of Pure and Applied Mathematics, 2024)
A hyper BN-algebra is a nonempty set H together with a hyperoperation ``’’ and a constant 0 such that for all x, y, z H: x x, x 0 = {x}, and (x y) z = (0 z) (y x), where x y if and only if 0 x y. We investigated the structures of ideals in the Hyper BN-algebra setting. We established equivalency of weak hyper BN-ideals and hyper subBN-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.