Definition:Field of Quotients

Let $$\left({D, +, \circ}\right)$$ be an integral domain.

Let $$\left({F, +, \circ}\right)$$ be a field.

Then $$\left({F, +, \circ}\right)$$ is a quotient field of $$\left({D, +, \circ}\right)$$ iff $$\left({F, +, \circ}\right)$$ contains $\left({D, +, \circ}\right)$ algebraically such that:


 * $$\forall z \in F: \exists x \in D, y \in D^*: z = \frac x y$$

where $$\frac x y$$ is $x$ divided by $y$.