Factoriality of the projective limit of factorial rings (Q913869)

The main result of this paper is the following: Let \((R_ n,i_ n)_{n\in {\mathbb{N}}}\) be a projective system of unique factorization domains; if \(i_{n+1}: R_{n+1}\to R_ n\) is epic and \(i^{- 1}_{n+1}(U(R_ n))=U(R_{n+1})\) for all \(n\in {\mathbb{N}}\), where \(U(R_ n)\) is the group of units of the ring \(R_ n\), then the projective limit \(\lim_{\leftarrow}R_ n \) is a unique factorization domain. Some applications of this result are given.