T-quasi continuous modules

• Published in: Quaestiones mathematicae Vol. 44; no. 3; pp. 399 - 409
• Main Authors: Adhami, Parastoo, Moghaderi, Javad, Tercan, Adnan
• Format: Journal Article
• Language: English
• Published: Grahamstown Taylor & Francis 04.03.2021; Taylor & Francis Ltd
• Subjects: Continuous modules; Modules; quasi-continuous modules; T-continuous modules; T-extending module; T-quasi continuous modules
• ISSN: 1607-3606; 1727-933X
• DOI: 10.2989/16073606.2019.1694596

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.