#### Vol. 2, 2019

 Recent Volumes 4: ANTS XIV 3: Hillman: Poincaré Duality 2: ANTS XIII 1: ANTS X
 The Open Book Series All Volumes About the Series Ethics Statement Purchase Printed Copies Author Index MSP Books and Monographs Other MSP Publications
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