Definition (quotient field):

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

Failed to parse (unknown function "\middle"): {\displaystyle \left\{\frac{a}{b} \middle| a \in R, b \in R^\times \right\}} ,

together with the multiplication and addition operations given by the formulae

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