Ore domain

Let $R$ be a domain (http://planetmath.org/IntegralDomain).We say that $R$ is a right Ore domainif 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 $xr=ys\eq 0$ .

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

The definition of a left Ore domain is similar.

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

单词	OreDomain
释义	Ore domain Let $R$ be a domain (http://planetmath.org/IntegralDomain).We say that $R$ is a right Ore domainif 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 $xr=ys\eq 0$ . This condition turns out to be equivalentto the following conditions on $R$ when viewed as a right $R$ -module: (a) $R_{R}$ is a uniform module. (b) $R_{R}$ is a module of finite rank. The definition of a left Ore domain is similar. If $R$ is a commutative domain (http://planetmath.org/IntegralDomain),then it is a right (and left) Ore domain.
随便看	ProjectionsAndClosedSubspaces projections and closed subspaces ProjectionsAsNoncommutativeCharacteristicFunctions projections as noncommutative characteristic functions ProjectionsOfAnalyticSetsAreAnalytic projections of analytic sets are analytic ProjectiveBasis projective basis ProjectiveCover projective cover ProjectiveCurve projective curve ProjectiveDimension projective dimension ProjectiveEquivalence projective equivalence ProjectiveGeometry projective geometry ProjectiveLineConfigurations projective line configurations ProjectiveModule projective module ProjectivePlane projective plane ProjectivePlaneOfATernaryRing