On maximal permutation BH—ideals of Permutation BH—Algebras

Abstract

New classes of algebras, like permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH$</tex> —algebra, permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH_{1}$</tex> —algebra, bounded permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH$</tex> —algebra, and normal permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH$</tex> —algebra are introduced. Next, their permutation ideals like, permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH$</tex> —ideal, maximal permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH_1$</tex> —ideal, and translation permutation BH-ideal are introduced and studied. Also, an equivalence relation ~ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</inf> is shown and the equivalence classes are discussed. A quotient permutation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$BH$</tex> —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.