Enumeration of quadrics of projective spaces over local rings (Q1759212)
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scientific article; zbMATH DE number 6108759
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Enumeration of quadrics of projective spaces over local rings |
scientific article; zbMATH DE number 6108759 |
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Enumeration of quadrics of projective spaces over local rings (English)
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20 November 2012
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Let \(R\) be a local ring such that 2 is a unit, the maximal ideal is nilpotent and \(R^ {\ast}\) contains precisely two square classes. Then the quadrics in a projective space over \(R\) were classified by \textit{G. P. Egorychev} and \textit{E. V. Zima} [Commun. Algebra 36, No. 4, 1426--1436 (2008; Zbl 1161.05304)] using the method of integral representations of combinatorial sums. In the present paper, the authors give an algebraic proof and an interpretation of this classification.
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local ring
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quadric
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projective space
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projective congruence
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