Ore theorem
= Ore theorem
{c}
A multiplicative set $S$ of <regular elements of a ring> admits a right ring of fractions exactly when it satisfies the <right Ore condition>. The resulting localization embeds the original <ring>, inverts $S$, and expresses every element as $as^{-1}$. For denominators that can be <zero divisors>, an additional denominator reversibility condition is required.