Euclidean domains with no multiplicative norms
Commutative Algebra
2025-03-11 v2 Rings and Algebras
Abstract
We construct a Euclidean domain with no multiplicative Euclidean norm to a compatibly well-ordered monoid, and hence with no multiplicative Euclidean norm to (under its usual order). A key step in the proof is showing that the UFD property is preserved when adjoining a free factorization.
Keywords
Cite
@article{arxiv.2501.05573,
title = {Euclidean domains with no multiplicative norms},
author = {Caleb J. Dastrup and Pace P. Nielsen},
journal= {arXiv preprint arXiv:2501.05573},
year = {2025}
}