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# Goldie ring

Let $R$ be a ring. If the set of annihilators
$\{\rann(x)\mid x\in R\}$
satisifies the ascending chain condition, then
$R$ 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 $R_{R}$ 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*.

Defines:

left Goldie, right Goldie, left Goldie ring, right Goldie ring

Related:

UniformDimension

Synonym:

Goldie

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

16P60*no label found*

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new question: Prime numbers out of sequence by Rubens373

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new question: how to contest an entry? by zorba

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new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag