Fundamental groups of topological $R$-modules

Abstract:

The main result of this paper is that if $R$ is a countable, Noetherian ring, then the underlying abelian group of every $R$-module is isomorphic to the fundamental group of some topological $R$-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 $V$.