# Definition:Ring Zero

## Definition

Let $\struct {R, +, \circ}$ be a ring.

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

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.

When the ring in question is also a field, the ring zero is called the field zero.

In the context of number fields, the ring zero is sometimes seen referred to as the additive identity.