Definition:Field Zero

Definition
Let $\struct {F, +, \times}$ be a field.

The identity for field addition is called the field zero (of $\struct {F, +, \times}$).

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

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

In the context of number fields, the field zero can also be referred to as the additive identity.

Also see

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