Modules with few types over a serial ring and over a commutative Prufer ring

摘要

It is proved that the theory of a module M over a countable serial ring has few models iff M is Sigma-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 Prufer ring has few types if and only if M is Sigma-pure-injective. [References: 18]