Definition:Division

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

Let the zero of $F$ be $0_F$.

The operation of division is defined as:


 * $\forall a, b \in F \setminus \set {0_F}: a / b := a \times b^{-1}$

where $b^{-1}$ is the multiplicative inverse of $b$.

The concept is usually seen in the context of the standard number fields:

Also see

 * Division Theorem for how the concept is extended to the integers


 * Definition:Divisor (Algebra)