On A Generalization of Small-Injective Modules

Authors

  • Zahraa Abbas Zone Mathematical Department , Education College, University of Al-Qadisiyah, Al-Diwaniya City, Iraq.
  • Akeel Ramadan Mehdi Mathematical Department/ College of Education/ University of Al-Qadisiyah https://orcid.org/0000-0003-1077-6489

DOI:

https://doi.org/10.24996/ijs.2024.65.5.24

Keywords:

JS-injective module, small-injective module, Noetherian module, projective module.

Abstract

        Let R be a ring. JS-injective right R-modules are introduced and studied in  this paper as a generalization of small-injective right R-modules. Let  N and  M be right R-modules. A module  M is said to be JS-N-injective if every  R-homomorphism from a submodule of J(N) J(R)  into  M extends to N. If a module M is JS-R-injective, then  M is called JS-injective. Many characterizations and properties of JS-injective right R-modules are obtained. Rings over which every right module is JS-injective are characterized. We study quotients of JS-injective right modules. Then we give conditions under which the class of  JS-injective right modules is closed under direct sums.

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Published

2024-05-30

Issue

Section

Mathematics

How to Cite

On A Generalization of Small-Injective Modules. (2024). Iraqi Journal of Science, 65(5), 2649-2658. https://doi.org/10.24996/ijs.2024.65.5.24

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