Two Ring is Boolean Ring

Theorem
Let $2$ be the two ring.

Then $2$ is a Boolean ring.

Proof
From Ring of Integers Modulo m, $2$ is a ring with unity.

Furthermore, the identities:


 * $0 \cdot 0 = 0$
 * $1 \cdot 1 = 1$

show that $2$ is also an idempotent ring.

Hence the result, by definition of Boolean ring.