Finite sets of affine points with unique associated monomial order quotient bases (Q2885386)
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scientific article; zbMATH DE number 6037673
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite sets of affine points with unique associated monomial order quotient bases |
scientific article; zbMATH DE number 6037673 |
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23 May 2012
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monomial order quotient basis
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Cartesian set
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zero-dimensional ideal
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Finite sets of affine points with unique associated monomial order quotient bases (English)
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The authors study the monomial order quotient bases of zero dimensional ideals of polynomials rings over the field \(\mathbb{F}\). They introduce two criteria through which we can check that the given zero dimensional ideal has a unique monomial order quotient bases or not. They also showed that the vanishing ideals of Cartesian sets have a unique monomial order quotient basis. Furthermore, they showed that there always exists at least one non-Cartesian point set in \(\mathbb{F}^d,\, d\geq 3\), whose vanishing ideal has a unique monomial order quotient basis.
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