nLab Ore domain




In algebra, a unital ring is an Ore domain if it is a domain RR in which the set R ×R^\times of all nonzero elements is an Ore set. Thus one can form the Ore localization R[(R ×) 1]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 RR[(R ×) 1]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 January 27, 2023 at 04:34:09. See the history of this page for a list of all contributions to it.