On Commutative and Medial of Bd-Algebras

Abstract

First of all, we begin this research by discussing the notion of B-algebras and d-algebras. Additionally, we provide some examples of it’s algebraic structure. The idea of Bd-Algebras, which combines characteristics from B-algebras and d-algebras, is then explained. An algebraic structure (X;*,0) is called Bd-algebras if for any r,s element of X satisfies the following axioms: r * 0 = r, and if r * s = 0 and s * r = 0 then r = s. We also provide the example about Bd-algebras. Next, we look at the definitions of commutative and medial in Bd-algebras. After that, we investigated some proporsitions about commutative and medial Bd-algebras. Then, we proven thats propositions. As an example, if (X;*,0) is a commutative and medial Bd-algebra, then (r * u) * (s * v) = (v * u) * (s * r) for any r,s,u,v element of X.