>>25
(and all others)
There is no such thing as "division" in the zero ring (or the trivial ring)
Rings are not required to have the property that every element has a multiplicative inverse. Therefore division is not defined for rings.
Otherwise we're talking about groups but even then division isn't defined because multiplication in groups isn't necessarily commutative so there really isn't any definable division "operator".
So it requires a FIELD to have division, and fields require additive identity != multiplicative identity, which makes the trivial ring {0} usless.
So division by the additive identity is never possible. QED