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# Ore condition

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

$ux=vy\quad\text{(resp.}xu=yv\text{).}$ |

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

Defines:

Ore ring, left Ore condition, right Ore condition, left Ore ring, right Ore ring

Related:

ClassicalRingOfQuotients,OresTheorem2

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

16U20*no label found*

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