A Class of Small Injective Modules

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