\begin{definition}[Definition:Multiplicative Identity]
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 $1$.
\end{definition}