A Class of Small Injective Modules
Journal of Al-Qadisiyah for Computer Science and Mathematics,
2018, Volume 10, Issue 3, Pages 141-150
AbstractLet 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.
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