Integral bases over $p$-adic fields
Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 509-520
Published online September 1, 2003
Alexandru Zaharescu
University of Illinois at Urbana-Champaign
Abstract : Let $p$ be a prime number, $\Q_p$ the field of $p$-adic numbers, $K$ a finite extension of $\Q_p$, $\bar K$ a fixed algebraic closure of $K$ and $\C_p$ the completion of $\bar K$ with respect to the $p$-adic valuation. Let $E$ be a closed subfield of $\C_p$, containing $K$. Given elements $t_1,\dots ,t_r\in E$ for which the field $K(t_1,\dots,t_r)$ is dense in $E$, we construct integral bases of $E$ over $K$.
Keywords : $p$-adic fields, integral bases, admissible polynomials
MSC numbers : 11S99
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