T-Stable-extending Modules and Strongly T- stable Extending Modules

Inaam Mohammed Ali  Hadi; Farhan Dakhil  Shyaa

doi:10.24996/ijs.2020.61.2.18

Authors

Inaam Mohammed Ali Hadi Department of Mathematics, University of Baghdad, College of Education for Pure Sciences (Ibn-Al-Haitham), University Of Baghdad, Iraq
Farhan Dakhil Shyaa Department of Mathematics, University of Al-Qadisiyah, College of Education, Al-Qadisiya, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.2.18

Keywords:

extending modules, S-extending module, t-stable extending modules, strongly t-stable extending modules

Abstract

In this paper we introduce the notions of t-stable extending and strongly t-stable extending modules. We investigate properties and characterizations of each of these concepts. It is shown that a direct sum of t-stable extending modules is t-stable extending while with certain conditions a direct sum of strongly t-stable extending is strongly t-stable extending. Also, it is proved that under certain condition, a stable submodule of t-stable extending (strongly t-stable extending) inherits the property.