Null Ring is Ring

Theorem
Let $R$ be the null ring.

That is, let:
 * $R := \struct {\set {0_R}, +, \circ}$

where ring addition and ring product are defined as:


 * $0_R + 0_R = 0_R$
 * $0_R \circ 0_R = 0_R$

Then $R$ is a ring.

Proof
A null ring is a trivial ring.

So, by Trivial Ring is Commutative Ring, the result follows.