Commutative B-Algebra is Entropic Structure

Theorem
Let $\struct {G, *}$ be a commutative $B$-algebra.

Then $\struct {G, *}$ is an entropic structure.

Proof
From Commutative $B$-Algebra Induces Abelian Group we have that there exists an abelian group $\struct {G, \circ}$ such that:


 * $\forall a, b \in G: a \circ b^{-1} = a * b$

where $a * b$ is defined by the binary operation in $\struct {G, *}$.

From Abelian Group Induces Entropic Structure, we have directly that $\struct {G, *}$ is an entropic structure.