Modules with Few Types Over A Serial Ring and Over A Commutative Prüfer Ring

Abstract

It is proved that the theory of a module M over a countable serial ring has few models iff M is ∑-pure—injective iff the theory of M has few types. It is also proved that the theory of a module M over a countable commutative Prüfer ring has few types if and only if M is ∑-pure—injective.