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.

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.