Reduced normal form of local integral bases
Number Theory
2016-04-25 v1
Abstract
We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal form: identification of isomorphic objects, construction of global bases by patching local ones, etc. but in addition the bases are reduced, which is a crutial property for several important applications. Except for very particular cases, a basis in Hermite normal form cannot be reduced.
Keywords
Cite
@article{arxiv.1604.06606,
title = {Reduced normal form of local integral bases},
author = {Nathália Moraes de Oliveira and Enric Nart},
journal= {arXiv preprint arXiv:1604.06606},
year = {2016}
}