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