Ore localization

Summary

Ore localization builds a ring of fractions $R S^{-1}$ of a noncommutative ring $R$. In it the elements of a chosen set $S$ become units, and every element has the form $a s^{-1}$. It exists when $S$ satisfies the Ore condition together with a reversibility condition. It extends the commutative localization and is the main tool to build division rings of fractions of noncommutative domains and classical rings of quotients.