On the arithmetical rank of monomial ideals (Q1100241)
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scientific article; zbMATH DE number 4042050
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the arithmetical rank of monomial ideals |
scientific article; zbMATH DE number 4042050 |
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On the arithmetical rank of monomial ideals (English)
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1988
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If I is an ideal of a commutative ring A, then the arithmetical rank of I, \(ara_ A I\), is the minimum number of elements of A generating I up to radical. The author proves the following theorem: Let A be the polynomial ring \(k [X_ 0,...,X_ n]\) in \(n + 1\) indeterminates, localized at \((X_ 0,...,X_ n)\), with k an infinite field, and let I be an ideal generated by monomials in the \(X_ i\) such that all its minimal prime ideals are of height \(\leq t\). Then \(ara_ A I \leq n + 1 - [n / t].\)
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monomial ideals
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symbolic Rees algebras
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number of generators of ideal
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arithmetical rank
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minimal prime ideals
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