Ore domain

Let R be a domain (http://planetmath.org/IntegralDomain). We say that R is a right Ore domain if any two nonzero elements of R have a nonzero common right multiple, i.e. for every pair of nonzero x and y, there exists a pair of elements r and s of R such that xr=ys0.

This condition turns out to be equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the following conditions on R when viewed as a right R-module:
(a) RR is a uniform module.
(b) RR is a module of finite rank.

The definition of a left Ore domain is similar.

If R is a commutativePlanetmathPlanetmathPlanetmathPlanetmath domain (http://planetmath.org/IntegralDomain), then it is a right (and left) Ore domain.

Title Ore domain
Canonical name OreDomain
Date of creation 2013-03-22 11:51:17
Last modified on 2013-03-22 11:51:17
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 11
Author antizeus (11)
Entry type Definition
Classification msc 16S10