Transfinitely valued Euclidean domains have arbitrary indecomposable order type
Commutative Algebra
2018-08-30 v2 Number Theory
Rings and Algebras
Abstract
We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely characterize the norm complexity of Euclidean domains. Modifying this construction, we also find a finitely valued Euclidean domain with no multiplicative integer valued norm.
Keywords
Cite
@article{arxiv.1703.02631,
title = {Transfinitely valued Euclidean domains have arbitrary indecomposable order type},
author = {Chris J. Conidis and Pace P. Nielsen and Vandy Tombs},
journal= {arXiv preprint arXiv:1703.02631},
year = {2018}
}
Comments
Accepted for publication at Communications in Algebra