A Necessary and Sufficient Condition for Uniqueness of Euclidean Division
Commutative Algebra
2026-04-30 v2 Number Theory
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.2604.24399,
title = {A Necessary and Sufficient Condition for Uniqueness of Euclidean Division},
author = {Senan Sekhon},
journal= {arXiv preprint arXiv:2604.24399},
year = {2026}
}
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7 pages