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单词 GoldieRing
释义

Goldie ring


Let R be a ring. If the set of annihilatorsPlanetmathPlanetmathPlanetmathPlanetmath{r.ann(x)xR}satisifies the ascending chain conditionMathworldPlanetmathPlanetmathPlanetmath, thenR is said to satisfy the ascending chain condition on right annihilators.

A ring R is called a right Goldie ring if it satisfies the ascending chain condition on right annihilators and RR is a module of finite rank.

Left Goldie ring is defined similarly. If the context makes it clear on which side the ring operates, then such a ring is simply called a Goldie ring.

A right Noetherian ring is right Goldie.

TitleGoldie ring
Canonical nameGoldieRing
Date of creation2013-03-22 14:04:10
Last modified on2013-03-22 14:04:10
Ownermclase (549)
Last modified bymclase (549)
Numerical id6
Authormclase (549)
Entry typeDefinition
Classificationmsc 16P60
SynonymGoldie
Related topicUniformDimension
Definesleft Goldie
Definesright Goldie
Definesleft Goldie ring
Definesright Goldie ring
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更新时间:2025/5/4 11:30:50