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.

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 21$: Example $21.4$