Definition:Multiplicative Inverse (Field Theory)

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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 $\dfrac 1 a$.

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