A minimal dimension polynomial of a field extension given by a system of linear differential equations (Q1823271)
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scientific article; zbMATH DE number 4114752
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A minimal dimension polynomial of a field extension given by a system of linear differential equations |
scientific article; zbMATH DE number 4114752 |
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A minimal dimension polynomial of a field extension given by a system of linear differential equations (English)
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1989
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The dimension polynomial (d.p.) of a field extension \(F\subset G\) is the Hilbert polynomial of the module of differentials \(\Omega_{G/F}\) associated with a certain system of generators of G over F. \textit{W. Sit} [Proc. Am. Math. Soc. 68, 251-257 (1978; Zbl 0391.12012)] introduced the notion of the minimal d.p. The present author computes d.p. for some examples and proves several necessary conditions for minimality of a d.p.
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Dirac equations
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dimension polynomial
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Hilbert polynomial
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module of differentials
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