Vol. 2, 2019

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Computation of triangular integral bases

Jens-Dietrich Bauch and Ha Thanh Nguyen Tran

Vol. 2 (2019), No. 1, 69–84
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.

Keywords
$\mathfrak{p}$-integral bases, maximal order, Montes algorithm, Dedekind domain
Mathematical Subject Classification 2010
Primary: 11Y16, 13B22
Milestones
Received: 1 March 2018
Revised: 20 June 2018
Accepted: 9 September 2018
Published: 13 February 2019
Authors
 Jens-Dietrich Bauch Department of Mathematics Simon Fraser University Burnaby, BC Canada Ha Thanh Nguyen Tran Department of Mathematics and Statistics University of Calgary Calgary, AB Canada