The Golomb topology of polynomial rings

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 is an algebraic extension of a nite eld and K′ is a eld of the same characteristic, then the Golomb spaces of K[X] and K ′ [X] are homeomorphic if and only if K and K′ are isomorphic.

Key words: Golomb topology, Dedekind domains, polynomial rings.