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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.
A right Noetherian ring is right Goldie.
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"Goldie ring" is owned by mclase.
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See Also: uniform dimension
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left Goldie, right Goldie, left Goldie ring, right Goldie ring |
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Cross-references: right noetherian ring, side, clear, module of finite rank, ascending chain condition, annihilators, ring
There is 1 reference to this entry.
This is version 3 of Goldie ring, born on 2003-11-22, modified 2003-11-23.
Object id is 5427, canonical name is GoldieRing.
Accessed 7209 times total.
Classification:
| AMS MSC: | 16P60 (Associative rings and algebras :: Chain conditions, growth conditions, and other forms of finiteness :: Chain conditions on annihilators and summands: Goldie-type conditions , Krull dimension) |
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Pending Errata and Addenda
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