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Ore condition (Definition)

A ring $ R$ satisfies the left Ore condition (resp. right Ore condition) if and only if for all elements $ x$ and $ y$ with $ x$ regular, there exist elements $ u$ and $ v$ with $ v$ regular such that

$\displaystyle ux = vy$   (resp.$\displaystyle xu = yv$).

A ring which satisfies the (left, right) Ore condition is called a (left, right) Ore ring.



"Ore condition" is owned by mclase.
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See Also: classical ring of quotients, Ore's theorem

Also defines:  Ore ring, left Ore condition, right Ore condition, left Ore ring, right Ore ring
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Cross-references: right, regular, ring
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This is version 3 of Ore condition, born on 2003-10-20, modified 2003-11-21.
Object id is 5403, canonical name is OreCondition.
Accessed 6378 times total.

Classification:
AMS MSC16U20 (Associative rings and algebras :: Conditions on elements :: Ore rings, multiplicative sets, Ore localization)

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