A [ring](Rings.md) defined on a [trivial group,](Groups.md#Trivial%20groups) $\{e\}$ is referred to as a _zero ring._ Given ring operators $+$ and $\cdot$ $e+e=e$ and $e\cdot e=e.$^404557 For any zero ring $0=1.$ #MathematicalFoundations/Algebra/AbstractAlgebra #MathematicalFoundations/Numbers