ABSTRACT
Abstract An example shows that if A = lim←− An is the inverse limit of an inverse system {ϕmn :Am → An | m ≥ n} of Be´zout (hence Pru¨fer) domains An , then A need not be a Pru¨fer (or a Be´zout) domain. If, however, each transition map ϕmn is surjective, the question whether A must be a Pru¨fer domain is more subtle. A partial result is given for this context. Enhancement of this result is considered by means of associated inverse systems of C P I -extensions, with applications to Pru¨fer domains, Be´zout domains and locally divided domains.
