Number of generators of a Cohen-Macaulay ideal. (Q1867310)
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scientific article; zbMATH DE number 1891321
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Number of generators of a Cohen-Macaulay ideal. |
scientific article; zbMATH DE number 1891321 |
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Number of generators of a Cohen-Macaulay ideal. (English)
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2 April 2003
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Let \(R\) be a noetherian local ring of embedding dimension \(v\). Let \(I\) be a Cohen-Macaulay ideal of \(R\) such that \(R/I\) has dimension \(d\) and multiplicity \(e \geq 3\). The main result of this paper proves that \(I\) can be generated by \((e-2)(v-d-1) + 2\) elements. This result can be extended to the non-local case by adding \(d\) more generators. There is a short but nice survey on previous results on the number of generators of ideals in Cohen-Macaulay local rings.
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number of generators
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Cohen-Macaulay ideal
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multiplicity
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embedding dimension
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