Definition:Null Ring

Definition
A ring with one element is called the null ring.

That is, the null ring is $\left({\left\{{0_R}\right\}, +, \circ}\right)$, where ring addition and the ring product are defined as:


 * $0_R + 0_R = 0_R$
 * $0_R \circ 0_R = 0_R$

Also see

 * Null Ring is Trivial Ring in which it is seen that the null ring is a trivial ring and therefore a commutative ring.


 * Non-Null Ring

Also known as
Some authors refer to this as the zero ring.

Others refer to it as the trivial ring, but this term has been defined differently elsewhere.