Totally indefinite Euclidean quaternion fields

@article{Jean2014,
abstract = {We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.},
author = {Jean-Paul Cerri, Jérôme Chaubert, Pierre Lezowski},
journal = {Acta Arithmetica},
keywords = {totally indefinite quaternion fields; Euclidean orders; norm-Euclidean orders},
language = {eng},
number = {2},
pages = {181-200},
title = {Totally indefinite Euclidean quaternion fields},
url = {http://eudml.org/doc/279728},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Jean-Paul Cerri
AU - Jérôme Chaubert
AU - Pierre Lezowski
TI - Totally indefinite Euclidean quaternion fields
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 2
SP - 181
EP - 200
AB - We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
LA - eng
KW - totally indefinite quaternion fields; Euclidean orders; norm-Euclidean orders
UR - http://eudml.org/doc/279728
ER -