"strongly N-extending Strongly N-extending Modules" by Saad Abdulkadhim Al-Saad and Darya Jaber Abdul-kareem

Article Title

strongly N-extending Strongly N-extending Modules

Authors

Saad Abdulkadhim Al-Saad, Department of Mathematics, College of Science, Al-Mustansiriyah University, IraqFollow
Darya Jaber Abdul-kareem, Ministry of Education -Diyala, IraqFollow

Document Type

Article

Abstract

Relative extending modules and relative (quasi-)continuous modules were introduced and studied by Oshiro as a generalizations of extending modules and (quasi-) continuous respectively. On other hand, Oshiro, Rizvi and Permouth introduced N-extending and N-(quasi-) continuous modules depending where N and M are modules. is closed under submodules, essential extension and isomorphic image. A module M is N-extending if for each submodule A , there is a direct summand B of M such that A is essential in B. Moreover, a module M is strongly extending if every submodule is essential in a stable (equivalently, fully invariant) direct summand of M. In this paper, we introduce and study classes of modules which are proper stronger than that of N-extending modules and N-(quasi-)continuous modules. Many characterizations and properties of these classes are given.

Keywords

strongly N-continuous, strongly N-qausi- continuous

Recommended Citation

Al-Saad, Saad Abdulkadhim and Abdul-kareem, Darya Jaber (2021) "strongly N-extending Strongly N-extending Modules," Al-Qadisiyah Journal of Pure Science: Vol. 26 : No. 4 , Article 33.
Available at: https://doi.org/10.29350/qjps.2021.26.4.1350