Extensions of the \(p\)-adic fields generated by the roots of a single polynomial in two variables (Q1570184)
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scientific article; zbMATH DE number 1471603
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extensions of the \(p\)-adic fields generated by the roots of a single polynomial in two variables |
scientific article; zbMATH DE number 1471603 |
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Extensions of the \(p\)-adic fields generated by the roots of a single polynomial in two variables (English)
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4 May 2002
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Let \(S\) be a set of extensions of a given degree of the \(p\)-adic field \(\mathbb{Q}_p\). It is shown that there exists a polynomial \(F(X,Y)\in \mathbb{Q}_p[X,Y]\) with the property that \(\{\mathbb{Q}_p(\theta_n): n=1,2,\dots\}=S\), where \(\theta_n\) is a root of \(F(n,Y)=0\).
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Hilbert's irreducibility theorem
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extensions of \(p\)-adic fields
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