# The Golomb topology on a Dedekind domain and the group of units of its quotients

@article{Spirito2019TheGT,
title={The Golomb topology on a Dedekind domain and the group of units of its quotients},
author={Dario Spirito},
journal={Topology and its Applications},
year={2019}
}
• D. Spirito
• Published 24 June 2019
• Mathematics
• Topology and its Applications

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Commentationes Mathematicae Universitatis Carolinae
• 2019
The Golomb space $\mathbb N_\tau$ is the set $\mathbb N$ of positive integers endowed with the topology $\tau$ generated by the base consisting of arithmetic progressions $\{a+bn\}_{n=0}^\infty$ with
In this note we would like to offer an elementary “topological” proof of the infinitude of the prime numbers. We introduce a topology into the space of integers S, by using the arithmetic
The theorem is remarkable, and gives some apparently counter-intuitive examples of spaces homeomorphic to the usual Q. Consider the “Sorgenfrey topology on Q,” which has the collection {(p, q] : p, q
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• 2019
Abstract In 1959 Golomb defined a connected topology on ℤ. An analogous Golomb topology on an arbitrary integral domain was defined first by Knopfmacher-Porubský [KP97] and then again in a recent
Euclid's proof of the infinitude of prime numbers is recast as a Euclidean criterion for a domain to have infinitely many atoms and it is shown that this criterion applies even in certain domains in which not all nonzero nonunits factor into products of irreducibles.
This is the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. It provides an introduction
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• 1969
* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *