Null Ring and Ring Itself Subrings

Theorem
In any ring $R$, the null ring and $R$ itself are subrings of $R$.

Proof

 * $R$ is a ring and $R \subseteq R$, so it follows trivially that $R$ is a subring of $R$.


 * The null ring $\left({\left\{{0_R}\right\}, +, \circ}\right)$ is always a ring, and a subset of $R$, so has to be a subring of $R$.