# Definition:Multiplicative Inverse (Field Theory)

## Definition

Let $\left({F, +, \times}\right)$ be a field whose zero is $0_F$.

Let $a \in F$ such that $a \ne 0_F$.

Then the inverse element of $a$ with respect to the $\times$ operator is called the multiplicative inverse of $F$.

It is usually denoted $a^{-1}$ or $\dfrac 1 a$.