Field Theory/Quotient fields

Definition (quotient field):

Let $R$ be an integral domain. The quotient field of $R$, often denoted $\operatorname {Frac} (R)$, is defined to be the field of formal fractions

$\left\{{\frac {a}{b}}|a\in R,b\in R^{\times }\right\}$,

together with the multiplication and addition operations given by the formulae

${\frac {a}{b}}{\frac {c}{c}}:={\frac {ac}{bd}}$ and ${\frac {a}{b}}+{\frac {c}{d}}:={\frac {ad+cb}{bd}}$.