New Classes of the Quotient Permutation BN-Algebras in Permutation BN-Algebras

The permutation BN-algebras have been given as a new class of algebras, and their basic features in this work were studied, with the aim of understanding how they relate to each other and how they can be used to form different types of superstructures. We looked at permutation BN-algebras, a form of {1}-commutative, condition (D), permutation BN-subalgebra, permutation BN-normal, and permutation BN1-algebra. Moreover, we explored some new notions in permutation theory for the first time. We also examined BN-algebra homomorphism, equivalence relations, quotient permutation BN-algebras, and BN-algebra isomorphism theorems.