Definition:B-Algebra

Definition
Let $\left({X, \circ}\right)$ be an algebraic structure.

Then $\left({X, \circ}\right)$ is a $B$-algebra iff:

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


 * $\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}$