## You are here

HomeOre condition

## Primary tabs

# 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*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith