2022/09/26 by Dario Spirito, Spirito, Dario
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics #General Topology (math.GN)
paper · pdf · doi:10.48550/arxiv.2209.12594
openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the set of irreducible polynomials of K[X] is dense in the Golomb space G(K[X]). We show that, in this case, the characteristic of K is a topological invariant, and that any self-homeomorphism of G(K[X]) is the composition of multiplication by a unit and a ring automorphism of K[X].