Definition:B-Algebra

Definition
Let $(X, \circ)$ be an algebraic structure.

Then $(X, \circ)$ is a B-algebra iff:

Example
This is a B-Algebra for the finite set $\{ 0,1,2,3,4,5\}$:


 * $\begin{array}{c|cccccc}

& 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 0 & 0 & 2 & 1 & 3 & 4 & 5 \\ 1 & 1 & 0 & 2 & 4 & 5 & 3 \\ 2 & 2 & 1 & 0 & 5 & 3 & 4 \\ 3 & 3 & 4 & 5 & 0 & 2 & 1 \\ 4 & 4 & 5 & 3 & 1 & 0 & 2 \\ 5 & 5 & 3 & 4 & 2 & 1 & 0 \\ \end{array}$