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 Z ₂-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.