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arXiv · 2305.16518

The unit fractions from a Euclidean domain generate a DVR

Neil Epstein
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Abstract

Let D be a Euclidean domain, with fraction field K. Let R(D) be the subring of K generated by the reciprocals of the nonzero elements of D. The main theorem states that if R(D) is not equal to K, then R(D) is a rank 1 discrete valuation ring that contains a field consisting of the units of D along with 0. Connections are made to ideas from medieval Italian mathematics.

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Neil Epstein. 2023-05-25. The unit fractions from a Euclidean domain generate a DVR. https://arxiv.org/abs/2305.16518

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