Null Ring is Ring

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Let $R$ be the null ring.

That is, let:

$R := \struct {\set {0_R}, +, \circ}$

where ring addition and ring product are defined as:

\(\ds 0_R + 0_R\) \(=\) \(\ds 0_R\)
\(\ds 0_R \circ 0_R\) \(=\) \(\ds 0_R\)

Then $R$ is a ring.


A null ring is a trivial ring.

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