On maximal permutation BH—ideals of Permutation BH—Algebras

New classes of algebras, like permutation
$BH$
—algebra, permutation
$BH_{1}$
—algebra, bounded permutation
$BH$
—algebra, and normal permutation
$BH$
—algebra are introduced. Next, their permutation ideals like, permutation
$BH$
—ideal, maximal permutation
$BH_1$
—ideal, and translation permutation BH-ideal are introduced and studied. Also, an equivalence relation ~
A
is shown and the equivalence classes are discussed. A quotient permutation
$BH$
—algebra is given and discussed its applications using homomorphism. Next, some notions are introduced and studied like permutation canonical mapping, and permutation medial part. Finally, some results in this work are stated and proved.