# 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.

 Title Ore condition Canonical name OreCondition Date of creation 2013-03-22 14:03:04 Last modified on 2013-03-22 14:03:04 Owner mclase (549) Last modified by mclase (549) Numerical id 6 Author mclase (549) Entry type Definition Classification msc 16U20 Related topic ClassicalRingOfQuotients Related topic OresTheorem2 Defines Ore ring Defines left Ore condition Defines right Ore condition Defines left Ore ring Defines right Ore ring