T-quasi continuous modules

Abstract

In this paper, we investigate the t-quasi continuous property for modules. It is proved that M is t-quasi continuous, if and only if M is a direct sum of a Z2-torsion module and a quasi-continuos module. Moreover we characterize the rings R for which certain R-modules are t-quasi continuous. We show that every R-module is t-quasi continuous, if and only if R(N) is t-quasi continuous, if and only if every
free R-module is t-quasi continuous.

Key words: Continuous modules, quasi-continuous modules, T-continuous modules, T-quasi continuous modules, T-extending module.