Classical right ring of quotients
= Classical right ring of quotients
{title2=$Q_{\mathrm{cl}}^r(R)=\{as^{-1}:a\in R,\ s\text{ regular}\}$}
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.