Definition:Multiplicative Identity

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

Then 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 $1$.

Note that the multiplicative identity of $F$ is the unity of the ring that $\struct {F, +, \times}$ is by definition of a field.