Zero ring
= Zero ring
{title2=$0=1$}
{wiki}
The ring with a single element, which is both its additive and multiplicative identity. If a unital <ring> has $0=1$, then every element $r$ equals $r1=r0=0$, so it is this ring. Under the usual definition it is excluded from <integral domains> and <fields>. The <quotient ring> $\mathbb Z/(1)$ is an example.