Abstract

The underlying modules of existentially closed ▵-algebras are studied. Among other things, it is proved that they are all elementarily equivalent, and that all of them are existentially closed as modules if and only if ▵ is regular. It is also proved that every saturated module in the appropriate elementary equivalence class underlies an e.c. ▵-algebra. Applications to some problems in module theory are given. A number of open questions are mentioned