Examples in noncommutative localization (Q1075409)
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scientific article; zbMATH DE number 3950749
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Examples in noncommutative localization |
scientific article; zbMATH DE number 3950749 |
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Examples in noncommutative localization (English)
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1986
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Let R be a Noetherian ring and Q its Goldie localization at a prime ideal P. Using ideas from [\textit{L. W. Small} and \textit{J. T. Stafford}, J. Algebra 70, 156-161 (1981; Zbl 0478.16012)], the authors construct (i) an example of a ring R, finitely generated as a module over its Noetherian centre, for which the localization Q at a maximal ideal is neither left nor right Noetherian and (ii) an example where Q is Noetherian on one side only.
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Noetherian ring
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Goldie localization
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prime ideal
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Noetherian centre
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maximal ideal
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