Classical right ring of quotients ($Q_{\mathrm{cl}}^r(R)=\{a{s}^{-1}:a\in R,s\text{ regular}\}$)

The classical right ring of quotients inverts all regular elements of a ring. Existence requires the right Ore condition for these denominators. The original ring embeds, every regular element becomes a unit, and every fraction has a right denominator. The right Ore condition also permits finitely many fractions to be placed over a common right denominator.