A Class of Small Injective Modules

  • Akeel Ramadan Mehdi Mathematical Department/ College of Education/ Al-Qadisiyah University/ Al-Diwaniya City/ Iraq
DOI: https://doi.org/10.29304/jqcm.2018.10.3.436
Keywords: Injective module, Definable class, a-small right ideal, Pure submodule.

Abstract

         Let  be a ring. In this paper, a right -module  is defined to be -injective if , for any annihilator-small right ideal  of . We characterize rings over which every right module is -injective. Conditions under which the class of -injective right -modules ( ) is closed under quotient (resp.  pure submodules, direct sums) are given. Finally, we study the definability of the class  

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Published
2018-09-26
How to Cite
Ramadan Mehdi, A. (2018). A Class of Small Injective Modules. Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(3), Math Page 141- 150. https://doi.org/10.29304/jqcm.2018.10.3.436
Issue
Vol 10 No 3 (2018)
Section
Math Articles