Vol. 2, 2019

Download this article
Download this article For screen
For printing
Recent Volumes
2: ANTS XIII
1: ANTS X
The Open Book Series
About the Series
Ethics Statement
 
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 A[x] a monic irreducible separable polynomial. For a given nonzero prime ideal p of A we present in this paper a new algorithm to compute a triangular p-integral basis of the extension L of K determined by f. This approach can be easily adapted to compute a triangular p-integral basis of fractional ideals I of the integral closure of A in L. Along this process one can compute 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