The Ore condition, named after the Norwegian mathematician, mathematician O. Ore, refers to a set of criteria in algebra that help identify whether a certain type of ring is integrally closed. More specifically, it is used to determine whether a finitely generated commutative algebra over a field is integrally closed in its field of fractions.
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The Ore condition is a common-multiple condition that permits fractions to be formed in a noncommutative ring.