Abstract

Let $A$ be a Dedekind domain, $K$ the fraction field of $A$, and $f\in A\left[x\right]$ a monic irreducible separable polynomial. For a given nonzero prime ideal $\mathfrak{p}$ of $A$ we present in this paper a new algorithm to compute a triangular $\mathfrak{p}$-integral basis of the extension $L$ of $K$ determined by $f$. This approach can be easily adapted to compute a triangular $\mathfrak{p}$-integral basis of fractional ideals $I$ of the integral closure of $A$ in $L$. Along this process one can compute $\mathfrak{p}$-integral bases for a family of ideals contained in $I$ as a by-product.

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Mathematical Subject Classification 2010

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