The unit fractions from a Euclidean domain generate a DVR
Commutative Algebra
2023-05-29 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.2305.16518,
title = {The unit fractions from a Euclidean domain generate a DVR},
author = {Neil Epstein},
journal= {arXiv preprint arXiv:2305.16518},
year = {2023}
}
Comments
7 pages. Comments welcome!