Ring theory

Ore condition

In mathematics, especially in the area of algebra known as ring theory, the Ore condition is a condition introduced by Øystein Ore, in connection with the question of extending beyond commutative rings the construction of a field of fractions, or more generally localization of a ring. The right Ore condition for a multiplicative subset S of a ring R is that for a ∈ R and s ∈ S, the intersection aS ∩ sR ≠ ∅. A (non-commutative) domain for which the set of non-zero elements satisfies the right Ore condition is called a right Ore domain. The left case is defined similarly. (Wikipedia).

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Related pages

Field of fractions | Integral domain | Flat module | Monoid ring | Mathematics | Principal ideal domain | Division ring | Free ideal ring | Bézout domain | Domain (ring theory) | Free monoid | Algebra | Noetherian ring | Zero divisor | Øystein Ore | Ring (mathematics) | Ring theory | Commutative ring