# Contents

## Definition

In algebra, a unital ring is an Ore domain if it is an integral domain (unital ring without zero divisors) $R$ in which the set $R^\times$ of all nonzero elements is an Ore set. Thus one can form the Ore localization $R[(R^\times)^{-1}]$ which is then a skew-field (division ring), called the Ore quotient ring (Ore quotient (skew)field). As Ore localizations of domains always do, it comes with a map $R\to R[(R^\times)^{-1}]$ which is 1-1. For most purposes, one sided Ore condition is sufficient, hence one considers also the weaker notions of left and right Ore domains.

category: algebra

Last revised on July 19, 2014 at 01:41:45. See the history of this page for a list of all contributions to it.