Definition:Ring Zero

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

The identity for ring addition is called the ring zero (of $\left({R, +, \circ}\right)$).

It is denoted $0_R$ (or just $0$ if there is no danger of ambiguity).

Also known as
When it is clear and unambiguous what is being discussed, the ring zero is often called just the zero.

Also see

 * In Ring Product with Zero, it is shown that the ring zero is a zero element for the ring product, thereby justifying its name as the zero of the ring.