Definition:Multiplicative Identity

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

The identity element of the multiplicative group $\struct {F^*, \times}$ of $F$ is called the multiplicative identity of $F$.

It is often denoted $e_F$ or $1_F$, or, if there is no danger of ambiguity, $e$ or $1$.

Also known as
The multiplicative identity of $F$ can also be referred to as the unity of $F$.

This arises from its roles as the unity of the ring that $\struct {F, +, \times}$ is by definition of a field.

The term unit is often used for unity.

It is preferred that this is not used on as it can be confused with a unit of a ring, which is a different thing altogether.

Also see

 * Definition:Unity of Semiring
 * Definition:Unity of Ring
 * Definition:Field Negative
 * Definition:Unit of Algebra