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A Class of Small Injective Modules | ||
| Journal of Al-Qadisiyah for Computer Science and Mathematics | ||
| Article 1, Volume 10, Issue 3, 2018, Pages 141-150 PDF (0 K) | ||
| Author | ||
| Akeel Ramadan Mehdi | ||
| Abstract | ||
| Let R be a ring. In this paper, a right R-module M is defined to be AS-injective if Ext1 (R ⁄K, M )=0 , for any annihilator-small right ideal K of R . We characterize rings over which every right module is AS-injective. Conditions under which the class of AS-injective right R-modules (ASIr ) is closed under quotient (resp. pure submodules, direct sums) are given. Finally, we study the definability of the class ASIr. | ||
| Keywords | ||
| Injective module; Definable class; small right ideal; Pure submodule | ||
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