On Associative Permutation BM-Algebras

The permutation BM -algebras has 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 BM -algebras a form of permutation coxeter algebra, permutation pre-coxeter algebra, and associative permutation BM-algebra. Moreover, we explored some new notions in permutation theory for the first time. We also examined the relationships between permutation BM-algebra and others classes of algebra like permutation
$B$
-algebra, and {1}-commutative permutation
$B$
-algebra.