Topological properties of inverse limits of free abelian monoids, with an application to inverse limits of UFDs (Q1806053)

The inverse limit of a system of commutative rings, indexed by \(\mathbb{N}\), is a topological ring under the inverse limit topology. Here the author considers the case where each of the rings is a unique factorisation domain and shows that every element of the inverse limit can be expressed uniquely (to within order and association) as a convergent countable product of irreducibles. This result is applied to the case of polynomial rings via a consideration of inverse limits of discretely topologised free abelian monoids.