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arXiv · 2501.05573

Euclidean domains with no multiplicative norms

Caleb J. Dastrup·Pace P. Nielsen
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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 $\mathbb{R}$ (under its usual order). A key step in the proof is showing that the UFD property is preserved when adjoining a free factorization.

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Caleb J. Dastrup, Pace P. Nielsen. 2025-03-08. Euclidean domains with no multiplicative norms. https://arxiv.org/abs/2501.05573

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