2019/06/24 by Dario Spirito, Spirito, Dario
Mathematics · #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #General Topology (math.GN) #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1906.09922
openalex publication_date 2019/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Golomb spaces of Dedekind domains with torsion class group. In\nparticular, we show that a homeomorphism between two such spaces sends prime\nideals into prime ideals and preserves the P-adic topology on R\∖ P.\nUnder certain hypothesis, we show that we can associate to a prime ideal P of\nR a partially ordered set, constructed from some subgroups of the group of\nunits of R/Pn, which is invariant under homeomorphisms, and use this result\nto show that the unique self-homeomorphisms of the Golomb space of \ℤ\nare the identity and the multiplication by -1. We also show that the Golomb\nspace of any Dedekind domain contained in the algebraic closure of \ℚ\nis not homeomorphic to the Golomb space of \ℤ.\n