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

  • 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
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.

Published
2020-02-28
How to Cite
Hadi, I. M. A., & Shyaa, F. D. (2020). T-Stable-extending Modules and Strongly T- stable Extending Modules. Iraqi Journal of Science, 61(2), 401-408. https://doi.org/10.24996/ijs.2020.61.2.18
Section
Mathematics