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.
Original language | English |
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Pages (from-to) | 1105-1113 |
Number of pages | 9 |
Journal | Communications in Algebra |
Volume | 47 |
Issue number | 3 |
DOIs | |
State | Published - Mar 4 2019 |
Externally published | Yes |
Funding
This work was supported by the National Security Agency [grant number H98230-16-1-0048].
Keywords
- Euclidean domain
- indecomposable ordinal
- multiplicative norm
- transfinitely valued