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Radicals of principal ideals and the class group of a Dedekind domain
- MathematicsPacific Journal of Mathematics
- 2021
For a Dedekind domain $D$, let $\mathcal{P}(D)$ be the set of ideals of $D$ that are radical of a principal ideal. We show that, if $D,D'$ are Dedekind domains and there is an order isomorphism…
The Golomb space is topologically rigid
- Mathematics
- 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 $\{a+bn:n\ge 0\}$ with…
Homeomorphisms of the space of non-zero integers with the Kirch topology
- Mathematics
- 2020
Abstract. The Golomb (resp. Kirch) topology on the set Z of nonzero integers is generated by the base consisting of arithmetic progressions a+ bZ = {a+ bn : n ∈ Z} where a ∈ Z and b is a…
The Golomb Topology of Polynomial Rings
- MathematicsQuaestiones Mathematicae
- 2020
Abstract We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show that if K…
The Golomb topology of polynomial rings, II
- Mathematics
- 2022
. We study the interplay of the Golomb topology and the algebraic structure in polynomial rings K [ X ] over a field K . In particular, we focus on infinite fields K of positive characteristic such that…
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