A Necessary and Sufficient Condition for Uniqueness of Euclidean Division
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908999347077120 |
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| author | Sekhon, Senan |
| author_facet | Sekhon, Senan |
| contents | A well-known result from the 1960s characterizes all Euclidean domains in which division is guaranteed to produce a unique quotient and remainder. As this relies on the historical (and more restrictive) definition of a Euclidean domain, the question of whether the result still holds under the modern definition was left open. In this paper, we prove the answer is afirmative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Necessary and Sufficient Condition for Uniqueness of Euclidean Division Sekhon, Senan Commutative Algebra Number Theory Rings and Algebras 13F07 (Primary), 13F20, 13F25, 11A05, 16U10 (Secondary) A well-known result from the 1960s characterizes all Euclidean domains in which division is guaranteed to produce a unique quotient and remainder. As this relies on the historical (and more restrictive) definition of a Euclidean domain, the question of whether the result still holds under the modern definition was left open. In this paper, we prove the answer is afirmative. |
| title | A Necessary and Sufficient Condition for Uniqueness of Euclidean Division |
| topic | Commutative Algebra Number Theory Rings and Algebras 13F07 (Primary), 13F20, 13F25, 11A05, 16U10 (Secondary) |
| url | https://arxiv.org/abs/2604.24399 |