Stable (quasi-) Continuous Modules

Abstract

In this paper, we introduce and study stable (quasi)- continuous modules as a proper generalization of (quasi)- continuous modules. Many results and properties of stable (quasi-)continuous modules are obtained. An R-module M is strongly (quasi-)continuous if and only if M is cl-fully stable and M is stable (quasi-)continuous. We verify some properties well-known for continuous modules still hold under Stable continuous modules. For instance, a directly finite stable continuous module is cohophfian.