Analysis of the \(2\)-d order curves over some finite ring (Q2880018)
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scientific article; zbMATH DE number 6022857
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analysis of the \(2\)-d order curves over some finite ring |
scientific article; zbMATH DE number 6022857 |
Statements
10 April 2012
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associative-commutative rings
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\(2\)-d order curves
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irregular points
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polynomial factorization
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canonical forms
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Analysis of the \(2\)-d order curves over some finite ring (English)
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The author investigates the \(2\)-d order curves over any finite associative-commutative ring with a unit. Conditions for the existence of irregular points are established. Sets of points of the investigated curves are characterized via polynomial factorization and relations imposed onto coefficients. Canonical forms for investigated curves are determined and methods of transforming of curves into these forms are investigated. The basic idea is the following. Linear transformations intended to annulate linear part of \(2\)-d order polynomial of two variables are characterized. Cases when these linear transformations are not bijections are extracted. Basic canonical quadric forms are determined. Methods for transformation any quadric form to canonical one are developed.
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