Fundamental groups of topological 𝑅-modules

Abstract

Abstract. The main result of this paper is that if R is a countable, Noetherian ring, then the underlying abelian group of every Ä-module is isomorphic to the fundamental group of some topological K-module. As a corollary, it is shown that for certain varieties V (e.g., varieties of finite type) every abelian group in V is isomorphic to the fundamental group of some arcwise connected topological algebra in V.